The impact of machine learning models on healthcare will depend on the degree
of trust that healthcare professionals place in the predictions made by these
models. In this paper, we present a method to provide people with clinical
expertise with domain-relevant evidence about why a prediction should be
trusted. We first design a probabilistic model that relates meaningful latent
concepts to prediction targets and observed data. Inference of latent variables
in this model corresponds to both making a prediction and providing supporting
evidence for that prediction. We present a two-step process to efficiently
approximate inference: (i) estimating model parameters using variational
learning, and (ii) approximating maximum a posteriori estimation of latent
variables in the model using a neural network, trained with an objective
derived from the probabilistic model. We demonstrate the method on the task of
predicting mortality risk for patients with cardiovascular disease.
Specifically, using electrocardiogram and tabular data as input, we show that
our approach provides appropriate domain-relevant supporting evidence for
accurate predictions.
Aniruddh Raghu araghu@mit.edu Eugene Pomerantsev Massachusetts General Hospital
Aniruddh Raghu araghu@mit.edu Eugene Pomerantsev Massachusetts General Hospital
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John Guttag
ジョン・グタグ(John Guttag)
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Massachusetts Institute of Technology
マサチューセッツ工科大学
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Adrian V. Dalca
Adrian V. Dalca
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Massachusetts Institute of Technology
マサチューセッツ工科大学
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Katherine Young Harvard Medical School Collin M. Stultz
Katherine Young Harvard Medical School Collin M. Stultz
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Massachusetts Institute of Technology Massachusetts General Hospital
マサチューセッツ工科大学マサチューセッツ総合病院
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Massachusetts Institute of Technology Massachusetts General Hospital
マサチューセッツ工科大学マサチューセッツ総合病院
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Harvard Medical School
ハーバード大学医学部
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Harvard Medical School
ハーバード大学医学部
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ABSTRACT The impact of machine learning models on healthcare will depend on the degree of trust that healthcare professionals place in the predictions made by these models.
In this paper, we present a method to provide individuals with clinical expertise with domain-relevant evidence about why a prediction should be trusted.
We present a two-step process to efficiently approximate inference: (i) estimating model parameters using variational learning, and (ii) approximating maximum a posteriori estimation of latent variables in the model using a neural network, trained with an objective derived from the probabilistic model.
We demonstrate the method on the task of predicting mortality risk for patients with cardiovascular disease.
本研究は,循環器疾患患者の死亡リスクを予測するための課題である。
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Specifically, using electrocardiogram and tabular data as input, we show that our approach provides appropriate domain-relevant supporting evidence for accurate predictions.
KEYWORDS Machine Learning, Interpretability ACM Reference Format: Aniruddh Raghu, John Guttag, Katherine Young, Eugene Pomerantsev, Adrian V. Dalca, and Collin M. Stultz.
KEYWORDS Machine Learning, Interpretability ACM Reference Format: Aniruddh Raghu, John Guttag, Katherine Young, Eugene Pomerantsev, Adrian V. Dalca, Collin M. Stultz。
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2021. Learning to Predict with Supporting Evidence: Applications to Clinical Risk Prediction.
2021. 支持証拠による予測への学習:臨床リスク予測への応用。
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In ACM Conference on Health, Inference, and Learning (ACM CHIL ’21), April 8–10, 2021, Virtual Event, USA.
ACM Conference on Health, Inference, and Learning (ACM CHIL’21), April 8–10, 2021, Virtual Event, USA。
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ACM, New York, NY, USA, 13 pages.
ACM, New York, NY, USA, 13ページ。
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https://doi.org/10.1 145/ 3450439.3451869 1 INTRODUCTION There is significant interest in using machine learning (ML) models in high-stakes domains such as medicine, where human experts use model predictions to inform decisions [6, 9, 46].
When used Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page.
Figure 1: Learning to Predict with Supporting Evidence.
図1:エビデンスをサポートすることで予測を学ぶこと。
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We propose a model that produces both a prediction and accompanying domain-relevant supporting evidence for that prediction: inferred concepts that are clinically meaningful and can assist a clinician in deciding how to act on the prediction.
Consistency of the prediction and supporting evidence is ensured using a probabilistic model and domain knowledge.
予測と証拠の一貫性は確率モデルとドメイン知識を使って保証される。
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by a clinician, the utility of an ML model depends not only on the accuracy of its predictions, but also on how much trust the clinician places in the prediction [42].
Building trust in predictions can be tackled in different ways, including (1) providing statistical arguments to reflect the level of certainty in a prediction [31, 35] (2) providing an explanation of how a model reached its prediction, either through understanding important input features that led to the model output, or by using an inherently explainable model [27, 43]; and (3) offering domainspecific supporting evidence about the prediction [13].
For models used by domain experts with a limited understanding of machine learning, prior work has emphasised the importance of providing domain-relevant supporting evidence for predictions [21, 28].
In medicine, presenting relevant clinical information that supports a model prediction can be crucial, since clinicians draw significantly on medical knowledge when making decisions [42, 45].
For example, a cardiologist might deem a patient to be at high risk of death (prediction) because of their low cardiac output (domain-relevant supporting evidence), which may inform a therapeutic choice [47].
ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA high risk of death) accompanied by clinically meaningful evidence for this prediction (e g , poor cardiac health) closely mirrors a clinician’s mental model when treating patients, helping to build trust.
ACM CHIL ’21, April 8-10, 2021, Virtual Event, USA high risk of death)は、この予測の臨床的に有意義な証拠(例えば、心臓の健康状態の悪化)を伴い、患者を治療する際の臨床医の精神モデルに密接に反映し、信頼を築くのに役立つ。
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In this paper, we present a method to construct predictive models that are accurate and provide domain-relevant supporting evidence for predictions (Figure 1).
The method is designed to provide users that have a deep understanding of the application domain with an appropriate reason to trust or distrust a prediction made by the model.
By construction, maximum a posteriori (MAP) inference in this probabilistic model yields both accurate predictions and domain-relevant supporting evidence.
(2) We demonstrate a two-step learning process that approximates MAP inference: (i) estimating parameters of the probabilistic model using variational learning; (ii) approximating MAP estimation of latent variables in the model, yielding a prediction and supporting evidence, using a neural network trained with an objective derived from the probabilistic model.
Importantly, we do not need labels for supporting concepts at training time.
重要なのは、トレーニング時に概念をサポートするラベルは必要ないことです。
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(3) We demonstrate our method on a real-world clinical dataset for the task of predicting mortality risk for patients with cardiovascular disease using multimodal electrocardiogram and tabular data.
We show that our method produces accurate risk predictions jointly with meaningful supporting evidence for predictions.
提案手法は,予測に対する有意義な支持証拠と協調して正確なリスク予測を行う。
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The supporting evidence captures information that is often only obtained from invasive procedures, and could provide important therapeutic insight for clinicians.
補助的証拠は、しばしば侵襲的処置からのみ得られる情報を捉え、臨床医に重要な治療的洞察を与える。
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2 RELATED WORK Work on improving trust has often focused on ML model interpretability, including post hoc interpretation using input feature attribution [25, 40, 43, 50]; post hoc concept-based attribution [10, 16]; and constructing explainable models through regularisation [27, 33] or prototype/input extraction [1, 22, 24].
Our work differs in spirit from these, since we: (1) do not focus on explaining how the predictive model works, and instead on providing explicit supporting evidence that is useful to domain experts with limited ML understanding; (2) embed a mechanism to provide supporting evidence for predictions directly into the model, rather than relying on post hoc analysis; and (3) use prior domain knowledge to inform the higher-level abstractions for supporting evidence, rather than learning abstractions that may not resemble inherently meaningful concepts.
Our work differs in spirit from these, since we: (1) do not focus on explaining how the predictive model works, and instead on providing explicit supporting evidence that is useful to domain experts with limited ML understanding; (2) embed a mechanism to provide supporting evidence for predictions directly into the model, rather than relying on post hoc analysis; and (3) use prior domain knowledge to inform the higher-level abstractions for supporting evidence, rather than learning abstractions that may not resemble inherently meaningful concepts.
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One closely related work is on Self-Explaining Neural Networks (SENN) [27], which provide explanations for predictions by forming predictions as a product of input-dependent concepts and weighting terms for these concepts.
The concepts for explanations are learned from data (not constrained by domain understanding) and are interpreted by considering input examples that most characterise them.
Unlike the supporting evidence we consider, learned concepts in SENN need not resemble meaningful abstractions that a domain expert would find useful in decision making.
The model relates the class label 𝑦𝑖 to (latent) class probability vector 𝜋𝑖, (latent) supporting evidence factors 𝑧𝑖, observed features for each data point 𝑥𝑖, and distributional parameters 𝜙 and 𝜓.
このモデルは、クラスラベル yi と (latent) クラス確率ベクトル πi 、(latent) 支持の証拠因子 zi 、各データポイント xi の観測された特徴、および分布パラメータ φ および (latent) と関連している。
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The circled quantities are random variables, with shading used for quantities observed at training time.
円周量はランダム変数であり、訓練時に観測された量にシェーディングを用いる。
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At inference time, we only observe the features 𝑥𝑖.
推測時、私たちは特徴 xi だけを観察します。
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The plate signifies variables that are data point-specific, for 𝑁 data points, and the quantities outside the plate are common across data points.
プレートは n 個のデータポイントに対してデータポイント固有の変数を意味し、プレート外の量はデータポイント間で共通である。
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uses input examples as prototypes to characterise learned concepts.
入力例をプロトタイプとして学習概念を特徴づけます。
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With complex, multimodal data, as in our clinical experiment, such examples can be challenging to visualise and understand.
臨床実験のように複雑なマルチモーダルデータでは、このような例は可視化と理解が難しい。
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Other recent work on using domain-relevant concepts to support predictions is close in spirit to ours [1, 13, 20], but these methods require labelled concepts at training time.
In contrast, our work relates the supporting concepts to the predictions through a probabilistic model, such that inference directly yields coupled predictions and supporting evidence for those predictions.
We detail further differences from related work (such as Koh et al [20], Melis and Jaakkola [27]) in the appendix.
付録中の関連する作品(Koh et al [20], Melis, Jaakkola [27] など)との相違について詳述する。 訳抜け防止モード: 関連作品(Koh et al [ 20 ] など)との相違について詳述する。 Melis and Jaakkola (27 ] ) in the appendix .
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3 LEARNING TO PREDICT WITH SUPPORTING EVIDENCE (LPS) In this section, we present our method, Learning to Predict with Supporting Evidence (LPS) , to construct models that produce both predictions and clinically-relevant supporting evidence.
3 LPSによる予測学習(LPS) 本論では, 予測と臨床関連証拠の両方を生成するモデルを構築するために, LPSによる予測学習(Learning to Predict with Supporting Evidence)について述べる。
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We define a probabilistic generative model that relates observed data, domain-relevant concepts, and predictive targets, specifying how to ground the concepts using a forward model.
Maximum a posteriori (MAP) inference in this model jointly yields predictions and domain-relevant supporting evidence.
このモデルにおける最大後部推定(MAP)は、予測とドメイン関連証拠を共同で生成する。
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Since such inference is computationally challenging, we present a two-step learning process to approximate MAP inference.
このような推論は計算的に困難であるため、MAP推論を近似する2段階の学習プロセスを提案する。
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3.1 Probabilistic Model We describe the model for a general binary classification problem, where the task is to predict class label 𝑦𝑖 and positive class probability 𝜋𝑖, given observed features 𝑥𝑖.
3.1 確率モデル 観測された特徴 xi を与えられたクラスラベル yi と正のクラス確率 πi を予測するタスクである一般二項分類問題のモデルを記述する。
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The model is summarised in Figure 2.
モデルは図2にまとめられます。
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英語（論文から抽出）
日本語訳
スコア
Learning to Predict with Supporting Evidence Formally, for 𝑖 = 1, .
i = 1 の証拠を形式的にサポートして予測する学習。
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. . , 𝑁 , the class label 𝑦𝑖 ∈ {0, 1} is distributed as 𝑦𝑖 ∼ Bernoulli(𝜋𝑖) where the positive class probability 𝜋𝑖 ∈ [0, 1] is distributed as the flexible prior 𝜋𝑖 ∼ Beta(𝛼, 𝛽).
. . N , N , クラスラベル yi ∈ {0, 1} は、正のクラス確率 πi ∈ [0, 1] が柔軟に先行する πi ∈ Beta(α, β) として分布する yi \ Bernoulli(πi) として分布する。
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Fixed parameters 𝛼 and 𝛽 capture the overall balance of the two classes.
固定パラメータ α と β は2つのクラスの全体のバランスを捉える。
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In clinical risk prediction, 𝜋𝑖 could represent an individual patient’s 60-day risk of death.
臨床リスク予測では、πiは患者の60日間の死亡リスクを表す可能性がある。
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We let 𝑧𝑖 ∈ R𝑚, 𝑧𝑖 ∼ 𝑝(𝑧𝑖|𝜋𝑖, 𝜙) be a latent vector encoding interpretable, domain-specific concepts, where 𝑚 is the number of concepts, and global parameters 𝜙.
zi ∈ Rm, zi , p(zi|πi, φ) を解釈可能で領域固有の概念を符号化する潜在ベクトルとし、m は概念の数、大域パラメータ φ である。
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The variable 𝑧𝑖 represents some clinically relevant concept that does not appear directly in the feature space, e g , estimated glomerular filtration rate (eGFR).
変数 zi は、例えば推定糸球体濾過率(egfr)のような特徴空間に直接現れない、臨床的に関係のある概念を表す。
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The observed features 𝑥𝑖 ∈ R𝑑, are distributed as 𝑥𝑖 ∼ 𝑝(𝑥𝑖|𝑧𝑖,𝜓), with global parameters 𝜓.
観測された特徴 xi ∈ rd は、大域パラメータ ψ を持つ xi(xi|zi,ψ) として分布する。
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In risk prediction, 𝑥𝑖 could be a patient’s creatinine, and low creatinine clearance is associated with low eGFR.
Domain-Relevant Supporting Evidence: We enforce that the variable 𝑧 encodes domain-relevant concepts by using a well-defined forward model, governed by domain knowledge, that characterises how some subset of the observations 𝑥 are generated from 𝑧.
ドメイン関連サポートエビデンス: 変数 z は、ドメイン知識が支配するよく定義されたフォワードモデルを用いて、z から観測 x のサブセットがどのように生成されるかを特徴付けることにより、ドメイン関連概念を符号化することを強制する。 訳抜け防止モード: ドメイン-関連サポートエビデンス : 変数 z がドメイン-関連概念を well-defined forward model を用いてエンコードすることを強制する。 ドメイン知識によって支配され 観測 x のサブセットが z から生成される様子を特徴づける。
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For example, the forward model could be a physiological model that relates observable values to latent cardiac function [7], atlas-based image deformation models [8], physics models [14], or many others.
We assume a prior 𝑝(𝜙) determined by domain understanding.
ドメイン理解によって決定される事前の p(φ) を仮定する。
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This modelling directly grounds 𝑧 to represent domain-relevant concepts by relating 𝑧 to 𝑥 via the forward model.
このモデリングは、Z と x をフォワードモデルを介して関連づけることで、z をドメイン関連の概念として直接表す。
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Consistency of 𝑧 and 𝜋 is enforced through the probabilistic model.
z と π の整合性は確率モデルを通じて強制される。
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We emphasise that the forward model need only characterise a sufficient subset of 𝑥 to constrain 𝑧; that is, we do not need to define a model to relate 𝑧 to all of 𝑥.
我々は、前進モデルは z を制約するために x の十分な部分集合のみを特徴づける必要があることを強調する;つまり、z を x のすべてに関連付けるモデルを定義する必要はない。
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This is advantageous and broadens LPS’s applicability because 𝑥 may be very high-dimensional and thus it may be challenging to define a forward model governing 𝑥 in its entirety.
In this work, we consider only smooth, continuous distributions for the domain knowledge, and a differentiable forward model.
この研究では、ドメイン知識の円滑で連続的な分布と差別化可能なフォワードモデルのみを検討する。
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In addition to being widely applicable, this enables tractable learning using gradient-based methods.
広く適用できるだけでなく、勾配に基づく手法による学習も可能である。
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3.2 Learning For a given observation 𝑥, we use maximum a posteriori (MAP) estimates of the class label 𝑦, its associated probability 𝜋, and the supporting concepts 𝑧: 𝜋∗, 𝑧∗, 𝑦∗ = arg max𝜋,𝑧,𝑦 = arg max𝜋,𝑧,𝑦
φ , z , y , arg max log p(π, z, y|x, φ ) , φ , φ , および近似 MAP の推定値: π , z , y , arg maxπ,z , y ログ p(π, z, y|x, φ , φ )。
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(4) Since the true posterior 𝑝(𝑧, 𝜋|𝑥, 𝑦,𝜓, 𝜙) is intractable, we cannot directly use the Expectation Maximization (EM) algorithm to estimate model parameters, because EM requires calculating this
(4) 真の後部p(z, π|x, y, φ) は可算であるため, モデルパラメータを推定するために期待最大化(英語版)(Expectation Maximization, EM)アルゴリズムを直接利用することはできない。
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ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA posterior exactly.
ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA posterior。
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We therefore resort to variational EM [5, 32] for parameter estimation: we define a variational approximation 𝑞(𝑧, 𝜋; 𝜃𝑞) to the true posterior with parameters 𝜃𝑞, and then construct a lower bound on the log evidence of data and model parameters as follows.
Instead, we use a network 𝑛(𝑥; 𝜃𝑛) → ( ^𝜋, ^𝑧) with parameters 𝜃𝑛 to efficiently approximate the MAP estimates such that: ^𝜋 ≈ 𝜋∗, ^𝑧 ≈ 𝑧∗, (8) ^𝑦 = 1 [ ^𝜋 ≥ 𝜂] ≈ 𝑦∗, (9) where 1[·] is an indicator function and 𝜂 is a threshold that depends on our desired tradeoff between recall and precision.
ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA supporting evidence ^𝑧 and prediction ^𝜋 is enforced by the MAP objective from the probabilistic model used to train the inference model (via the term 𝑝(^𝑧| ^𝜋)).
ACM CHIL ’21, April 8-10, 2021, virtual Event, USA support evidence ^z and prediction ^π is enforceed by the MAP objective from the probabilistic model used to training the inference model (via the term p(^z| ^π)。
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To recover 𝜋∗, 𝑧∗, 𝑦∗ given a test example 𝑥, we directly use 𝑛(𝑥; 𝜃∗ 𝑛) to obtain the MAP estimates using (8), and (9).
3.4 Discussion on Modelling Representation of domain knowledge: In some clinical settings, domain knowledge is typically represented using hard constraints or thresholds.
For example, one definition of sepsis uses hard thresholds of a severity score [41].
例えば、敗血症の定義は重症度スコア[41]のハードしきい値を使用する。
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However, it is often the case that a continuous distribution is often a more realistic representation of the relationship between relevant concepts and the prediction task.
For example, the relationship between severity scores and risk of mortality is well represented as a smooth, continuous function, since higher severity scores correlate with higher risk in a smooth fashion.
Generality of the model: This class of models is appropriate for a range of binary classification problems because the Beta distribution is a flexible distribution for 𝜋 and the distributions 𝑝(𝑧|𝜋, 𝜙) and 𝑝(𝑥|𝑧,𝜓) can be specified as desired.
Using a Dirichlet prior for 𝜋 and a multinomial for 𝑦 is a natural extension of this model to the multiclass scenario.
π に対して dirichlet prior と y に対する multinomial を用いることは、このモデルの多クラスシナリオへの自然な拡張である。
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In this paper, we focus on binary classification for clinical risk stratification.
本稿では,臨床リスク階層化のためのバイナリ分類に着目する。
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Supporting Evidence vs.
Evidence vs. のサポート。
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Explanations: Since there is no guarantee that there is a causal link between ^𝑧 and the prediction ^𝜋, we refer to ^𝑧 as providing supporting evidence for the prediction rather than explaining the prediction.
4 RISK PREDICTION IN REAL-WORLD We instantiate and demonstrate LPS on the task of predicting a cardiovascular patient’s risk of mortality within the 6 months following a cardiac event.
4 リスク予測 in REAL-WORLD 心臓イベント後の6ヶ月以内に心血管疾患の死亡リスクを予測するタスクでLPSをインスタンス化し、実証します。
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We show that LPS produces accurate risk predictions and informative supporting evidence.
我々は,LSSが正確なリスク予測と情報的支援証拠を生成することを示す。
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Code implementing LPS is available at https://github.com/a niruddhraghu/lps.
Cardiovascular disease affects a large number of people worldwide, and is a major cause of mortality [4].
心臓血管疾患は世界中で多くの人に影響を与え、死亡の大きな原因となっている[4]。
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Predicting mortality risk for patients with cardiovascular disease is an important task that has received significant prior study in the medical literature [2, 11, 26, 29, 30, 34, 37].
In this section, we focus on predicting patient risk and providing supporting evidence for predictions from electrocardiogram (ECG) and tabular data, which are observed for many cardiology patients in hospital settings.
4.1 Data The dataset we use has 3728 patients from the Massachusetts General Hospital, is de-identified, and was obtained with IRB approval.
このデータセットを使用する4.1データは、マサチューセッツ総合病院の3728人の患者で、識別不能となり、irbの承認を得た。 訳抜け防止モード: 4.1 データセットは マサチューセッツ総合病院の患者3728人です de - 識別され、irb承認で取得されます。
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Each patient has undergone a cardiac catheterisation, which we treat as the index event.
それぞれの患者は心臓カテーテル治療を受けており、指標イベントとして扱われる。
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Each patient in the dataset has the following measurements and demographic features recorded: 12-lead electrocardiogram (ECG), heart rate (HR), systolic blood pressure, diastolic blood pressure, ethnicity, age, and gender.
4.2 Model Instantiation We let 𝑥 be the ECG and the tabular features, summarised in Figure 3, and 𝑦 the mortality outcome.
4.2 Model Instantiation x を ECG と表形式の特徴とし、図 3 に要約し、y を死亡率の結果とする。
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The risk 𝜋 is the probability of 𝑦.
リスク π は y の確率である。
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We let 𝑧 ∈ R5 be a vector of clinically important quantities: systemic vascular resistance (𝑅), arterial compliance (𝐶), systole time (𝑇𝑠), diastole time (𝑇𝑑), and cardiac output (𝐶𝑂).
z ∈ R5 を臨床的に重要な量のベクトルとする:全身血管抵抗性(R)、動脈適合性(C)、収縮時間(Ts)、ジアストール時間(Td)、および心臓出力(CO)。
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These quantities are not observed for many patients; for some, such as 𝑅, 𝐶, and 𝐶𝑂, this is because accurate direct measurement is invasive [3], and estimating them in (non-invasive) physical exams is challenging [12].
This mixture form for each component implies the following definition of the parameters: 𝑧𝑚,0}.
各コンポーネントのこの混合形式は、パラメータの次の定義を意味する: zm,0}。
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, 𝜇𝑧𝑚,0, 𝜎 2
, 𝜇𝑧𝑚,0, 𝜎 2
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𝜙𝑧𝑚 = {𝜇𝑧𝑚,1, 𝜎 2 𝑧𝑚,1
𝜙𝑧𝑚 = {𝜇𝑧𝑚,1, 𝜎 2 𝑧𝑚,1
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This instantiation for the distribution has an intuitive interpretation of generating each latent variable 𝑧𝑚 for each patient as a mixture of two components, weighted by the patient’s risk of death.
ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA
ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA
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Figure 3: Multimodal data for each patient in our clinical dataset: a 12-lead ECG and 8 tabular features.
図3: 臨床データセットにおける各患者のマルチモーダルデータ: 12個の心電図と8個の表状特徴。
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. We now specify how each of these parameters are determined for each component of 𝑧: • 𝑅: Take the roughly 20% of patients in the training dataset that have recorded values for 𝑅.
For these patients, fit a lognormal distribution to the resulting 𝑅 values.
これらの患者に対しては、対数正規分布を結果のR値に適合させる。
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The parameters of this fitted distribution become ˜𝜇𝑅,1 and ˜𝜎 2 .
この適応分布のパラメータは、μr,1 および σ 2 となる。
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Repeat this process for the subset of patients 𝑅,1 that lived; the resulting parameters are ˜𝜇𝑅,0 and ˜𝜎 2 𝑅,0 • 𝐶: No patients have measured values for 𝐶 (vascular compliance is never directly measured).
Approximately estimate the time constant 𝜏 = 𝑅𝐶 for each patient in the training dataset for which we have 𝑅 recorded.
Rを収録したトレーニングデータセットにおいて,各患者の時間定数 τ = RC を推定した。
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This is done by using the diastole relation from the two element Windkessel model [7] to relate the systolic and diastolic pressures to the time constant.
Divide this resulting time constant by 𝑅 to get approximate values for 𝐶.
この結果の時間定数を R で割って C の近似値を得る。
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Then, determine parameters by following the same process as with determining distributions for 𝑅.
そして、R の分布を決定するのと同じプロセスに従ってパラメータを決定する。
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• 𝑇𝑠: No patients have measured values for 𝑇𝑠.
Ts: Tsの値を測定した患者はいません。
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Approximately estimate these by using the fact that 𝑇𝑠 is approximately 1/3 of the duration of a heart beat (reciprocal of heart rate, recorded for all patients).
Having estimated these on the training dataset, follow the same process as with 𝑅 to determine parameters.
トレーニングデータセットでこれらを推定すると、Rと同じプロセスに従ってパラメータを決定する。
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• 𝑇𝑑: No patients have measured values for 𝑇𝑑.
• Td: Tdの値を測定した患者はいません。
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Approximately estimate these by using the fact that 𝑇𝑑 is approximately 2/3 of the duration of a heart beat (reciprocal of heart rate, recorded for all patients).
Specification for 𝑝(𝑥|𝑧,𝜓): We partition 𝑥 into two components: (1) 𝑥 (𝑔), which is generated from 𝑧 based on a known forward model 𝑔(𝑧); and (2) 𝑥 (𝑓 ), which is formed from 𝑧 based on a forward model 𝑓 (𝑧,𝜓) with parameters 𝜓 that cannot be specified with current domain knowledge, and is thus learned from data.
p(x|z,ψ): 既知のフォワードモデルg(z)に基づいてzから生成されるx(g)と、現在のドメイン知識では指定できないパラメータψを持つフォワードモデルf(z,ψ)に基づいてzから形成されるx(f)の2つのコンポーネントにxを分割し、データから学習する。 訳抜け防止モード: p(x|z,...) の仕様 : x を 2 つの成分に分割する: ( 1 ) x ( g ) これは既知のフォワードモデル g(z ) に基づいて z から生成される。 そして、 ( 2 ) x ( f ) は、現在のドメイン知識では特定できないパラメータ t を持つフォワードモデル f ( z, i ) に基づいて z から生成される。 データから学習するのです
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We let 𝑥 (𝑔) represent the vital signs (heart rate and blood pressures) and 𝑥 (𝑓 ) capture the remaining features.
我々は、x (g) がバイタルサイン(心拍数と血圧)を表し、x (f ) が残りの特徴をとらえる。
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We define: 𝑝(𝑥 (𝑔)|𝑧,𝜓) = N(𝑔(𝑧), 0.12), where the known forward model 𝑔(·) has two components: (1) the two element Windkessel model to model the blood cretely, 𝑔(𝑧) → (𝐵𝑃sys,𝐵𝑃dias,(cid:99)𝐻𝑅), corresponding to the estimated pressures using a differential equation [7, 38, 48]; and (2) the definition of the heart rate based on systolic and diastolic times.
Conmeans for the end systolic pressure, end diastolic pressure, and heart rate respectively.
末期収縮圧, 末期拡張圧, 心拍数について検討した。
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These are produced as follows:
これらは以下のとおりである。
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• Two element Windkessel model: this is a differential equation model that models the evolution of the blood pressure waveform as a function of the latent variables 𝑅, 𝐶,𝑇𝑠,𝑇𝑑, and 𝐶𝑂.
• 2要素ウィンドケッセルモデル:これは、血圧波形の進化を潜在変数 R, C, Ts, Td, CO の関数としてモデル化する微分方程式モデルである。
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This model separately characterises the systole phase, where blood is ejected out of the heart through the aorta as a result of ventricular contraction, and the diastole phase, where blood flows into the ventricles at the start of the next cardiac cycle.
We adopt the formulation from Catanho et al [7], and the blood pressure in each phase is modelled as follows: 𝑑𝑃(𝑡) + 𝑃(𝑡) = 𝐼(𝑡), (cid:16) 𝜋𝑡 (cid:17) (cid:40)𝐼0 sin 𝐶 𝑑𝑡 𝑅 during systole 𝑇𝑠 during diastole.
私たちはCatanho et al [7] の定式化を採用し、各相の血圧は次の通りモデル化される: dP(t) + P(t) = I(t), (cid:16) πt (cid:17) (cid:40)I0 sin C dt R during systole Ts during diastole。
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0 𝐼(𝑡) = where
0 𝐼(𝑡) = どこに
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𝐼(𝑡) represents the input blood flow, with a half-sinusoid model used for systole, and zero-input for diastole.
By definition, stroke volume can be expressed in terms of cardiac output and heart rate 𝐻𝑅 = (𝑇𝑠+𝑇𝑑)×𝐶𝑂 (cid:18) 𝜋𝑡 (cid:19) ∫ 𝑇𝑠 , and we obtain the following expression 𝑆𝑉 = 𝐶𝑂 60 for 𝐼0: 𝜋 𝐶𝑂 (𝑇𝑠 + 𝑇𝑑) (𝑇𝑠 + 𝑇𝑑)𝐶𝑂 =⇒ 𝐼0 = 𝑑𝑡 = 𝑆𝑉 = 𝐼0 sin 120𝑇𝑠 𝑇𝑠 60 𝑡=0 Note that 𝜋 in these equations refers to the mathematical constant, and not the patient’s risk of mortality.
定義によれば、ストローク体積は心拍出力と心拍数 HR = (Ts+Td)×CO (cid:18) πt (cid:19) > Ts で表すことができ、次の式 SV = CO 60 for I0: π CO (Ts + Td) CO = π I0 = dt = SV = I0 sin 120Ts Ts 60 t=0 これらの方程式のπは、患者の死亡リスクではなく、数学的定数を指す。
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With these governing differential equations, we use the piecewise of time.
これらの支配的な微分方程式では、時間の区分を用いる。
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To obtain the desired quantities, 𝐵𝑃sys and𝐵𝑃dias, we solutions for the blood pressures in each phase from Catanho et al [7].
所望の量を得るため,カタンホおよびアル[7]から各段階の血圧を算出した。 訳抜け防止モード: 所望の量を得る。 BPsys and BPdias, we solution for the blood pressures in each phase from Catanho et al [7 ]。
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This solution specifies the blood pressure as a function step forward the solution for 4 cardiac cycles (each cycle is of duration 𝑇𝑠 +𝑇𝑑) so that it reaches steady state.
We then evaluate cycles to produce𝐵𝑃sys and𝐵𝑃dias.
次に BPsys と BPdias を生成するサイクルを評価します。
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Note that the computation the solution at intervals of 𝑇𝑠 and 𝑇𝑑 for a further 6 cycles, and average the end systolic and diastolic pressures from these 6 .
For the ECG, we let 𝜎𝑓 = 5, and for the remaining features, we
ECGの場合、σf = 5 とし、残りの機能については、
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60 𝑇𝑠+𝑇𝑑 .
60 𝑇𝑠+𝑇𝑑 .
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ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA let 𝜎𝑓 = 0.5.
ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA let σf = 0.5。
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More details on network architecture are provided in Section 4.5 and in the appendix.
ネットワークアーキテクチャの詳細は第4.5節と付録に記載されている。
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4.4 Learning and Inference As described in Section 3, LPS has two stages: firstly, we obtain approximate MAP estimates ^𝜙∗ and ^𝜓∗ for model parameters (learning phase); secondly, we train another predictive model to efficiently output MAP estimates for latent model variables (inference phase), yielding a risk prediction and domain-relevant supporting evidence.
We use variational EM to derive approximate MAP estimates ^𝜙∗ and ^𝜓∗.
変動 EM を用いて近似 MAP 推定値 ^φ と ^ を導出する。
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We use a deep neural network to model the variational the variational posterior as5 posterior 𝑞(𝑧, 𝜋|𝑥; 𝜃𝑞).
深部ニューラルネットワークを用いて、変分後続の変分後続のq(z, π|x; θq)をモデル化する。
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Again denoting the components of 𝑧 as 𝑧𝑚, 𝑚 = 1, .
再び z の成分を zm, m = 1 として表す。
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. . , 5, we use a mean field approximation and factor 𝑞(𝑧𝑚|𝑥)𝑞(𝜋|𝑥).
. . , 5 では平均場近似と因子 q(zm|x)q(π|x) を用いる。
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Each 𝑞(𝑧𝑚|𝑥) is 𝑚=1 defined to be a log normal distribution, and 𝑞(𝜋|𝑥) to be a Beta distribution.
それぞれの q(zm|x) は m=1 で対数正規分布、q(π|x) はベータ分布と定義される。
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The variational posterior network takes the ECG and tabular features as input, and produces mean and variance estimates for the posterior of each 𝑧𝑚, and Beta concentration parameter estimates for the posterior of 𝜋.
We approximate the expectation in (6) by drawing a single sample from the variational posterior using the reparameterisation trick [18, 36], enabling end-to-end gradient-based training.
After running variational EM, we recover approximate MAP estimates ^𝜙∗ and ^𝜓∗.
変動 EM を実行した後、近似 MAP 推定 ^φ と ^φ を回復する。
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For efficient MAP inference of latent variables, we train a MAP neural network 𝑛(𝑥; 𝜃𝑛) to take in the ECG and tabular features and directly output MAP estimates of 𝑧 and 𝜋.
This is trained using the objective in Equation 10.
これは10等式で目的を用いて訓練される。
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Further details on learning and inference are in the appendix.
学習と推論に関するさらなる詳細は付録にある。
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4.5 Neural Network Architectures We now outline the architectures for the three neural networks involved in this LPS instantiation: the learned forward model 𝑓 , the variational posterior 𝑞, and the MAP inference network 𝑛.
• Learned forward model 𝑓 (𝑧,𝜓): this takes as input 𝑧 and uses fully connected layers for the tabular features, and a 1D convolutional network with upsampling layers for the ECG.
• 学習された前方モデル f (z, ) は入力 z であり、表層の特徴に対して完全に連結された層と、ECG のアップサンプリング層を持つ 1D 畳み込みネットワークを使用する。
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• Variational posterior 𝑞(𝑧, 𝜋|𝑥; 𝜃𝑞): this takes as input the ECG and tabular features, 𝑥.
• 変分後 q(z, π|x; θq): これは ECG と表特徴 x を入力として取る。
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The ECG is passed through a 1D convolution residual network, and the tabular features through a two layer fully connected network.
These representations are concatenated and passed through additional fully connected layers to produce mean and variance estimates for the posterior of each 𝑧𝑚 and Beta concentration parameter estimates for the posterior of 𝜋.
• MAP inference network 𝑛(𝑥; 𝜃𝑛): this is a neural network with the same architecture as the variational posterior network, except that it directly outputs the MAP estimates of 𝑧 and 𝜋, rather than distributional parameters.
Further architectural and training details are in the appendix.
さらなるアーキテクチャとトレーニングの詳細は付録にある。
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4.6 Experiment Details Performance Baselines: We train a network with the same architecture as 𝑛(𝑥; 𝜃𝑛) to predict only the class label without the supporting evidence.
We use this to investigate whether simultaneously learning to predict and supporting evidence impacts the quality of the prediction.
これを用いて,同時学習による予測と支援が予測の質に影響を及ぼすかどうかを検討する。
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We use SENN [27] as a second baseline,
SENN[27]を第2のベースラインとして使用します。
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A. Raghu, et al which both predicts and provides information designed to supplement the prediction.
a. raghu, et al はどちらも予測を補完するために設計された情報を予測し、提供する。
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Ablation: As an ablation, we consider a variant of LPS that we call LPS-𝑞.
アブレーション: アブレーションとして LPS-q と呼ばれる LPS の変種を考える。
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Here, instead of training a separate MAP inference network 𝑛(𝑥; 𝜃𝑛), we take the variational posterior 𝑞(𝑧, 𝜋|𝑥; 𝜃𝑞) and use the mode of this posterior to obtain MAP estimates for 𝑧 and 𝜋.
The modes of the respective log normal and Beta distributions have simple analytical forms in terms of the distributional parameters that are output by the variational posterior network, so are easy to compute.
This simpler variant does not require training a separate MAP inference network.
この単純な変種は、別々のMAP推論ネットワークをトレーニングする必要はない。
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Evaluation: We use the median/half IQR for ten runs, splitting the dataset into ten train/validation/tes t sets (60%/20%/20%), and Welch’s 𝑡-test for statistical significance.
4.7 Results Table 1 summarises the results on the clinical dataset.
4.7 結果表 1 臨床データセットの結果を要約する。
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While we focus on analysing the supporting evidence, we also find that LPS, SENN, and the baseline perform comparably in terms of AUC, and that LPS-𝑞 performs worse than LPS, justifying the use of the MAP inference network.
Thus, it may sacrifice accuracy in recovering the modes to better represent the distribution as a whole.
したがって、分布全体をより良く表現するためにモードを復元する精度を犠牲にする可能性がある。
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Accuracy of supporting evidence. We first compare the accuracy of the supporting information for the ∼ 80% of patients that have 𝐶𝑂 measurements.
証拠の正確さ。 まず,CO測定を行った患者の80%の患者を対象に,支援情報の精度を比較した。
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We compare how the estimated 𝐶𝑂 compares to the measured 𝐶𝑂 by splitting 𝐶𝑂 into two groups using a cutoff of 4 L/min, which corresponds to the lower limit of normal range for 𝐶𝑂 [15] – a clinical standard that informs practice.
Computing the resulting F1 score, we observe that LPS estimates do a good job of differentiating between patients who have low and normal cardiac outputs (Table 1).
Since 𝐶𝑂 is usually estimated using invasive procedures and is important in clinical decision making, the fact that LPS can (non-invasively) identify when 𝐶𝑂 is above/below a meaningful threshold is clinically valuable.
Too few patients have measurements of the other latent variables (cid:99)𝐻𝑅 (from 𝑇𝑠 and 𝑇𝑑) and the blood pressures(cid:99)𝐵𝑃 from the estimated to enable a meaningful direct comparison.
In lieu of doing this, we use the known forward model to reconstruct both the heart rate latent values.
これを行う代わりに、既知のフォワードモデルを使用して、心拍潜伏値の両方を再構築します。
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We observe high coefficient of determination between the reconstructed quantities and the measured values for HR and BP (Table 1).
再構成量とHRおよびBPの測定値との間に高い決定係数を観測する(表1)。
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This suggests effective recovery of the latent parameters.
これは潜在パラメータの効果的な回復を示唆する。
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As further analysis, Figure 4 visualises the true blood pressures and heart rate, and the reconstructed estimates from the forward model using the inferred latent concepts from the model.
the heart rate (cid:99)𝐻𝑅 and blood pressure(cid:99)𝐵𝑃 from the supporting evidence, the reconstructions capture most of the variance of Table 1: LPS predictions and supporting evidence are accurate.
Figure 4: Reconstructing observed tabular features using the forward model.
図4:前方モデルを用いた観測表の特徴の再構成。
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We visualise the true blood pressures and heart rate vs. the reconstructed blood pressures and heart rate calculated from the inferred latent concepts using the forward model.
前方モデルを用いて推定潜伏概念から算出した真の血圧と心拍数と再建された血圧と心拍数を可視化します。
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The true and reconstructed quantities show good agreement, indicating successful recovery of the latent factors.
真の再構成量は良好な一致を示し、潜在的な要因の回復に成功したことを示す。
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Figure 5: Supporting evidence concepts and risk predictions have distributions that are in alignment with domain understanding.
図5: エビデンスの概念とリスク予測のサポートには、ドメインの理解と一致する分布があります。
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Empirical distributions (histograms) of clinically meaningful factors for patients in the upper and lower quartiles of predicted risk are in accordance with clinical domain knowledge.
Such agreement is important for supporting evidence and predictions to be trusted by clinicians [42, 45].
この合意は臨床医 [42, 45] に信頼される証拠や予測を支持する上で重要である。
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output and higher systemic vascular resistance relative to those who do not have adverse outcomes [44].
有害な結果を持っていない人に対する出力およびより高い全身性血管抵抗[44]。
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This is recovered by LPS, achieving consistency of predictions and supporting evidence with clinical domain knowledge.
これはLPSによって回復され、予測の一貫性を達成し、臨床ドメイン知識を持つ証拠をサポートする。
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Comparing supporting evidence.
支持証拠を比較する。
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Figure 6 shows supporting evidence for model decisions from LPS and attributions from Integrated Gradients [43], a commonly used feature attribution method, on the baseline.
We compare LPS and Integrated Gradients for two patients, one at high risk of death (top), and one at low risk of death (bottom).
死亡リスクが高い患者(上)と死亡リスクが低い患者(下)の2例について,LPSと統合勾配を比較した。
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LPS produces supporting evidence that is clinically understandable, specifically that the patient shown at the top is at high risk and has elevated 𝑅 and low 𝐶𝑂.
These statements give insights beyond the feature space alone.
これらのステートメントは、機能空間だけを超えて洞察を与えます。
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In contrast, the baseline of Integrated Gradients reveals certain features in the tabular data and the ECG that contributed to the decision, but the attributions are not as readily actionable as the supporting evidence from LPS.
For example, the patient in Figure 6 had a normal heart rate (HR) of 80 bpm (normal
例えば、図6の患者は、通常の心拍数(HR)が80 bpm(正常)であった。
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ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA
ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA
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A. Raghu, et al
A. Raghu, et al
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Figure 6: Supporting evidence from LPS is comprehensible and provides actionable insights.
図6: LPSからのエビデンスのサポートは理解でき、実行可能な洞察を提供する。
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In comparison to attribution methods such as Integrated Gradients, LPS produces supporting evidence that is clinically meaningful and provide insights beyond the input feature space.
For a high risk patient (top), LPS produces actionable supporting evidence, namely that that 𝐶𝑂 and 𝑅 (which are hard to observe and important in therapeutic decisions) lie outside their normal ranges.
For a low risk patient (bottom), LPS recovers supporting evidence factors within their normal ranges.
低いリスクの患者(下)のために、LPSは正常な範囲内の支持の証拠の要因を回復します。
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This supporting evidence for a prediction is actionable and less ambiguous than feature attribution methods such as Integrated Gradients, especially when applied to a high-dimensional input such as the ECG.
Figure 7: LPS supporting evidence could provide actionable insights on challenging, borderline cases.
図7:LPSサポートの証拠は挑戦的な、ボーダーライン場合の実用的な洞察を提供することができます。
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The patient shown had an adverse outcome (𝑦 = 1), but was predicted by LPS to be at low risk – a misclassification.
患者は、副作用(y = 1)があったが、LPSによって低リスクであると予測された - 誤分類。
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Analysing the weak supporting evidence for this decision adds more insight.
この決定に対する弱い支持証拠を分析することは、さらなる洞察をもたらす。
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range: 60-100 bpm), yet the HR feature contributed significantly to the prediction of high risk.
範囲: 60-100 bpm) であったが,HRの特徴は高いリスクの予測に大きく寄与した。
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It is unlikely that knowing that the HR was a factor in the model’s prediction would lead to any action on the part of a clinician.
HRがモデルの予測の要因であることを知ることは、臨床医のあらゆる行動につながる可能性は低い。
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For the low risk patient (bottom), LPS’s supporting evidence for a prediction of low risk is accompanied by the inference that the patient has normal 𝐶𝑂 and 𝑅.
Integrated gradients analysis reveals that most of the tabular features and the QRS complex of the ECG contribute to a low risk prediction, but the HR, recorded as 60 bpm, elevates the patient’s risk.
For a clinician who is not an ML practitioner, it may be challenging to disentangle these different factors and thus understand/trust the model’s predictions using the Integrated Gradients attribution.
Such explanatory insights are challenging to obtain from existing explainability methods.
このような説明的洞察は、既存の説明可能性手法から得ることが困難である。
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Patient-specific insights from supporting evidence.
証拠支援からの患者固有の洞察。
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Figure 8 compares supporting evidence for a pair of patients predicted to be at high risk.
図8は、リスクが高いと予測された患者のペアの支持証拠を比較します。
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The predictions and supporting evidence are clinically meaningful: on the left, the patient has high 𝑅, and on the right,
予測と支持の証拠は臨床的に有意義です。左側は患者の高いRを持ち、右側は患者です。
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Learning to Predict with Supporting Evidence
エビデンスのサポートによる予測の学習
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ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA
ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA
0.96
Figure 8: LPS supporting evidence offers patient-specific insights to clinicians.
図8:LPSサポート証拠は臨床医に患者固有の洞察を提供します。
0.66
For two patients who were predicted to be at high risk ( ^𝜋 > 0.8) LPS supporting evidence captures different factors contributing to risk, potentially informing clinicians of the most suitable patient-specific medical interventions.
the patient has low 𝐶𝑂, both of which are typically indicative of poor cardiovascular health [15, 44].
患者は低いCOを持ち、どちらも通常、心臓血管の健康状態が悪いことを示す[15, 44]。
0.77
LPS supporting evidence is well-differentiated on a per-patient basis and could inform a clinician that the left patient could benefit from medication to reduce 𝑅, and the right patient could benefit from medication to increase 𝐶𝑂.
5 CONCLUSION To assist human experts in decision making, machine learning models should produce both accurate predictions and supporting evidence for these predictions.
In healthcare, this consideration is particularly important since clinicians draw significantly on medical principles in their decision making, and therefore can act most effectively on predictions that are accompanied by clinically relevant supporting evidence.
To tackle this problem, we propose a method, Learning to Predict with Supporting Evidence (LPS), to construct models that provide both predictions and supporting evidence using clinically-relevant concepts.
この問題を解決するために,臨床関連概念を用いて予測と証拠の双方を提供するモデルを構築するためのLPS(Learning to Predict with Supporting Evidence)を提案する。
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We demonstrate that LPS produces accurate predictions and comprehensible supporting evidence for predictions on a realworld medical dataset.
LPS relies on domain knowledge to inform (1) the choice of concepts for supporting evidence, and (2) how these concepts are related to the observed data and the prediction.
LPS could be applied to other prediction problems by leveraging such medical domain knowledge, helping to further the trustworthiness and actionability of machine learning models for healthcare.
It is important that prior to any deployment, extensive user studies are performed in order to detect such issues and prevent potential negative impact.
The authors thank the members of the Clinical and Applied Machine Learning group and the Computational Cardiovascular Research group at MIT for all their helpful comments and advice.
REFERENCES [1] Maruan Al-Shedivat, Avinava Dubey, and Eric P Xing.
REFERENCES [1] マルアン Al-Shedivat、Avinava Dubey、Eric P Xing。
0.72
2017. Contextual explanation networks.
2017. 文脈説明ネットワーク。
0.76
arXiv preprint arXiv:1705.10301 (2017).
arXiv preprint arXiv:1705.10301 (2017)
0.84
[2] Elliott M Antman, Marc Cohen, Peter JLM Bernink, Carolyn H McCabe, Thomas Horacek, Gary Papuchis, Branco Mautner, Ramon Corbalan, David Radley, and Eugene Braunwald.
[2] Elliott M Antman, Marc Cohen, Peter JLM Bernink, Carolyn H McCabe, Thomas Horacek, Gary Papuchis, Branco Mautner, Ramon Corbalan, David Radley, Eugene Braunwald
0.78
2000. The TIMI risk score for unstable angina/non–ST elevation MI: a method for prognostication and therapeutic decision making.
2006. Comparison of invasive and less-invasive techniques of cardiac output measurement under different haemodynamic conditions in a pig model.
2006. 豚モデルにおける異なる血行動態条件下での心臓出力測定の侵襲的および低侵襲的手法の比較
0.81
European journal of anaesthesiology 23, 1 (2006), 23–30.
european journal of anaesthesiology 23, 1 (2006), 23–30。
0.85
[4] Emelia J Benjamin, Paul Muntner, Alvaro Alonso, Marcio S Bittencourt, Clifton W Callaway, April P Carson, Alanna M Chamberlain, Alexander R Chang, Susan Cheng, Sandeep R Das, et al 2019.
Emelia J Benjamin, Paul Muntner, Alvaro Alonso, Marcio S Bittencourt, Clifton W Callaway, April P Carson, Alanna M Chamberlain, Alexander R Chang, Susan Cheng, Sandeep R Das, et al 2019。
0.76
Heart disease and stroke Statistics-2019 update a report from the American Heart Association.
(2003). [6] Carrie J Cai, Emily Reif, Narayan Hegde, Jason Hipp, Been Kim, Daniel Smilkov, Martin Wattenberg, Fernanda Viegas, Greg S Corrado, Martin C Stumpe, et al 2019.
(2003). 6] Carrie J Cai, Emily Reif, Narayan Hegde, Jason Hipp, Been Kim, Daniel Smilkov, Martin Wattenberg, Fernanda Viegas, Greg S Corrado, Martin C Stumpe, et al 2019。
0.84
Human-centered tools for coping with imperfect algorithms during medical decision-making.
医療意思決定における不完全なアルゴリズムに対処するための人間中心ツール。
0.58
In Proceedings of the 2019 CHI Conference on Human Factors in Computing Systems.
2019 chi conference on human factors in computing systemsの開催中である。
0.72
1–14. [7] Marianne Catanho, Mridu Sinha, and Varsha Vijayan.
2012. Model of aortic blood flow using the windkessel effect.
2012. ウィンドケッセル効果を用いた大動脈血流モデル
0.76
(2012). [8] Adrian V Dalca, Evan Yu, Polina Golland, Bruce Fischl, Mert R Sabuncu, and Juan Eugenio Iglesias.
(2012). 8]Adrian V Dalca, Evan Yu, Polina Golland, Bruce Fischl, Mert R Sabuncu, Juan Eugenio Iglesias。
0.78
2019. Unsupervised deep learning for Bayesian brain MRI segmentation.
2019. ベイズ脳MRIにおける教師なし深層学習
0.78
In International Conference on Medical Image Computing and Computer-Assisted Intervention.
international conference on medical image computing and computer-assisted intervention にて発表。
0.81
Springer, 356–365. [9] Maria De-Arteaga, Riccardo Fogliato, and Alexandra Chouldechova.
356-365頁。 9] Maria De-Arteaga、Riccardo Fogliato、Alexandra Chouldechova。
0.60
2020. A Case for Humans-in-the-Loop: Decisions in the Presence of Erroneous Algorithmic Scores.
2020. human-in-the-loop: 誤ったアルゴリズムスコアの存在下での決定。
0.73
In Proceedings of the 2020 CHI Conference on Human Factors in Computing Systems.
2020 chi conference on human factors in computing systems で開催されている。
0.76
Association for Computing Machinery, 1–12.
アソシエーション・フォー・コンピューティング・マシンズ, 1-12。
0.58
[10] Amirata Ghorbani, James Wexler, James Y Zou, and Been Kim.
Amirata Ghorbani氏、James Wexler氏、James Y Zou氏、Been Kim氏。
0.70
2019. Towards automatic concept-based explanations.
2019. 概念に基づく自動説明。
0.85
In Advances in Neural Information Processing Systems.
神経情報処理システムの進歩です
0.58
9273–9282.
9273–9282.
0.71
[11] Christopher B Granger, Robert J Goldberg, Omar Dabbous, Karen S Pieper, Kim A Eagle, Christopher P Cannon, Frans Van de Werf, Alvaro Avezum, Shaun G Goodman, Marcus D Flather, et al 2003.
11] Christopher B Granger, Robert J Goldberg, Omar Dabbous, Karen S Pieper, Kim A Eagle, Christopher P Cannon, Frans Van de Werf, Alvaro Avezum, Shaun G Goodman, Marcus D Flather, et al 2003。
0.82
Predictors of hospital mortality in the global registry of acute coronary events.
急性冠疾患の世界登録簿における病院死亡率の予測要因
0.73
Archives of internal medicine 163, 19 (2003), 2345–2353.
archives of internal medicine 163, 19 (2003), 2345–2353。
0.83
[12] Bart Hiemstra, Geert Koster, Renske Wiersema, Yoran M Hummel, Pim van der Harst, Harold Snieder, Ruben J Eck, Thomas Kaufmann, Thomas WL Scheeren, Anders Perner, et al 2019.
12] Bart Hiemstra, Geert Koster, Renske Wiersema, Yoran M Hummel, Pim van der Harst, Harold Snieder, Ruben J Eck, Thomas Kaufmann, Thomas WL Scheeren, Anders Perner, et al 2019。
0.82
The diagnostic accuracy of clinical examination for estimating cardiac index in critically ill patients: the Simple Intensive Care Studies-I.
重症心疾患患者における心指数推定のための臨床検査の診断精度:簡易集中治療研究-I
0.83
Intensive care medicine 45, 2 (2019), 190–200.
集中治療薬45, 2 (2019), 190–200。
0.74
[13] Michael Hind, Dennis Wei, Murray Campbell, Noel CF Codella, Amit Dhurandhar, Aleksandra Mojsilović, Karthikeyan Natesan Ramamurthy, and Kush R Varshney.
13] Michael Hind, Dennis Wei, Murray Campbell, Noel CF Codella, Amit Dhurandhar, Aleksandra Mojsilović, Karthikeyan Natesan Ramamurthy, Kush R Varshney
0.72
2019. TED: Teaching AI to explain its decisions.
2019. TED: 意思決定を説明するためにAIを教える。
0.78
In Proceedings of the 2019
2019年の議事録では
0.63
英語（論文から抽出）
日本語訳
スコア
ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA
ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA
0.96
A. Raghu, et al
A. Raghu, et al
0.99
483–526 (1899).
483–526 (1899).
0.88
Journal of molecular and cellular cardiology 22, 3 (1990), 253–254.
journal of molecular and cellular cardiology 22, 3 (1990), 253–254。
0.83
[39] N Saouti, N Westerhof, PE Postmus, and A Vonk-Noordegraaf.
2013. Deep inside convolutional networks: Visualising image classification models and saliency maps.
2013. 畳み込みネットワークの奥深く:画像分類モデルと塩分マップを可視化する。
0.84
arXiv preprint arXiv:1312.6034 (2013).
arXiv preprint arXiv:1312.6034 (2013)。
0.76
[41] Mervyn Singer, Clifford S Deutschman, Christopher Warren Seymour, Manu Shankar-Hari, Djillali Annane, Michael Bauer, Rinaldo Bellomo, Gordon R Bernard, Jean-Daniel Chiche, Craig M Coopersmith, et al 2016.
41] Mervyn Singer, Clifford S Deutschman, Christopher Warren Seymour, Manu Shankar-Hari, Djillali Annane, Michael Bauer, Rinaldo Bellomo, Gordon R Bernard, Jean-Daniel Chiche, Craig M Coopersmith, et al 2016
0.88
The third international consensus definitions for sepsis and septic shock (Sepsis-3).
敗血症と敗血症性ショックの第3次国際コンセンサス定義(sepsis-3)。
0.65
JAMA 315, 8 (2016), 801–810.
JAMA 315, 8 (2016), 801–810。
0.90
[42] Collin M Stultz.
[42]Colin M Stultz。
0.71
2019. The Advent of Clinically Useful Deep Learning.
[43] Mukund Sundararajan, Ankur Taly, and Qiqi Yan.
[43]Mukund Sundararajan,Ankur Taly,Qiqi Yan。
0.64
2017. Axiomatic attribution for deep networks.
2017. 深層ネットワークに対する公理的帰属
0.77
In Proceedings of the 34th International Conference on Machine Learning-Volume 70.
34th International Conference on Machine Learning-Volume 70の進捗状況
0.78
JMLR. org, 3319–3328.
JMLR所属。 享年3319-3328。
0.57
[44] Thenappan Thenappan, Kurt W Prins, Marc R Pritzker, John Scandurra, Karl Volmers, and E Kenneth Weir.
44] thenappan Thenappan, Kurt W Prins, Marc R Pritzker, John Scandurra, Karl Volmers, E Kenneth Weir。
0.77
2016. The critical role of pulmonary arterial compliance in pulmonary hypertension.
2016. 肺高血圧症における肺動脈コンプライアンスの重要性
0.85
Annals of the American Thoracic Society 13, 2 (2016), 276–284.
Annals of the American Thoracic Society 13 2 (2016), 276–284。
0.80
[45] Sana Tonekaboni, Shalmali Joshi, Melissa D McCradden, and Anna Goldenberg.
Sana Tonekaboni氏、Shalmali Joshi氏、Melissa D McCradden氏、Anna Goldenberg氏。
0.68
2019. What Clinicians Want: Contextualizing Explainable Machine Learning for Clinical End Use.
2019. 臨床医が望むもの: 臨床終末のための説明可能な機械学習のコンテキスト化。
0.74
In Machine Learning for Healthcare Conference.
In Machine Learning for Healthcare Conference に参加。
0.87
359–380. [46] Eric J Topol.
359–380. [46] Eric J Topol
0.70
2019. High-performance medicine: the convergence of human and artificial intelligence.
2019. 高性能医療:人間と人工知能の融合。
0.76
Nature medicine 25, 1 (2019), 44–56.
自然医学25, 1 (2019), 44–56。
0.74
[47] Jean-Louis Vincent and Daniel De Backer.
[47]Jean-Louis VincentとDaniel De Backer。
0.93
2013. Circulatory shock.
2013. 循環ショック。
0.73
New England Journal of Medicine 369, 18 (2013), 1726–1734.
New England Journal of Medicine 369, 18 (2013), 1726–1734。
0.87
[48] Nico Westerhof, Jan-Willem Lankhaar, and Berend E Westerhof.
[48] Nico Westerhof、Jan-Willem Lankhaar、Berend E Westerhof。
0.81
2009. The arterial windkessel.
2009. 動脈のウィンドケセル
0.75
Medical & biological engineering & computing 47, 2 (2009), 131–141.
Medical & Bio Engineering & Computing 47, 2 (2009), 131–141。
0.81
[49] Clyde W Yancy, Mariell Jessup, Biykem Bozkurt, Javed Butler, Donald E Casey, Mark H Drazner, Gregg C Fonarow, Stephen A Geraci, Tamara Horwich, James L Januzzi, et al 2013.
49] Clyde W Yancy, Mariell Jessup, Biykem Bozkurt, Javed Butler, Donald E Casey, Mark H Drazner, Gregg C Fonarow, Stephen A Geraci, Tamara Horwich, James L Januzzi, et al 2013。
0.82
2013 ACCF/AHA guideline for the management of heart failure: executive summary: a report of the American College of Cardiology Foundation/American Heart Association Task Force on practice guidelines.
2013 ACCF/AHA guideline for the management of heart failure: Executive summary: a report of the American College of Cardiology Foundation/American Heart Association Task Force on Practice Guidelines。
0.92
Journal of the American College of Cardiology 62, 16 (2013), 1495–1539.
Journal of the American College of Cardiology 62, 16 (2013), 1495–1539。
0.84
[50] Matthew D Zeiler and Rob Fergus.
50] Matthew D ZeilerとRob Fergus。
0.71
2014. Visualizing and understanding convolutional networks.
2014. 畳み込みネットワークの可視化と理解。
0.80
In European conference on computer vision.
コンピュータビジョンに関する欧州会議で。
0.79
Springer, 818–833. AAAI/ACM Conference on AI, Ethics, and Society.
818-833頁。 AI、倫理、社会に関するAAAI/ACM会議。
0.67
123–129. [14] Yuanming Hu, Luke Anderson, Tzu-Mao Li, Qi Sun, Nathan Carr, Jonathan Ragan-Kelley, and Frédo Durand.
[20] Pang Wei Koh, Thao Nguyen, Yew Siang Tang, Stephen Mussmann, Emma Pierson, Been Kim, and Percy Liang.
20] Pang Wei Koh, Thao Nguyen, Yew Siang Tang, Stephen Mussmann, Emma Pierson, Been Kim, Percy Liang。
0.73
2020. Concept Bottleneck Models.
2020. コンセプトボトルネックモデル。
0.79
arXiv preprint arXiv:2007.04612 (2020).
arXiv preprint arXiv:2007.04612 (2020)。
0.75
[21] Todd Kulesza, Simone Stumpf, Margaret Burnett, Sherry Yang, Irwin Kwan, and Weng-Keen Wong.
Todd Kulesza, Simone Stumpf, Margaret Burnett, Sherry Yang, Irwin Kwan, and Weng-Keen Wong。
0.71
2013. Too much, too little, or just right?
2013. 多すぎる、小さすぎる、またはちょうど正しいですか?
0.82
Ways explanations impact end users’ mental models.
方法の説明はエンド ユーザーの精神モデルに影響を与えます。
0.58
In 2013 IEEE Symposium on Visual Languages and Human Centric Computing.
2013年、IEEE Symposium on Visual Languages and Human Centric Computing に参加。
0.81
IEEE, 3–10.
IEEE 3-10。
0.85
[22] Tao Lei, Regina Barzilay, and Tommi Jaakkola.
22] Tao Lei、Regina Barzilay、Tommi Jaakkola。
0.59
2016. Rationalizing neural predictions.
2016. 神経予測の合理化。
0.75
arXiv preprint arXiv:1606.04155 (2016).
arXiv preprint arXiv:1606.04155 (2016)。
0.76
[23] Andrew S Levey, Lesley A Stevens, Christopher H Schmid, Yaping Zhang, Alejandro F Castro III, Harold I Feldman, John W Kusek, Paul Eggers, Frederick Van Lente, Tom Greene, et al 2009.
23] Andrew S Levey, Lesley A Stevens, Christopher H Schmid, Yaping Zhang, Alejandro F Castro III, Harold I Feldman, John W Kusek, Paul Eggers, Frederick Van Lente, Tom Greene, et al 2009。
0.82
A new equation to estimate glomerular filtration rate.
糸球体濾過率を推定する新しい方程式
0.66
Annals of internal medicine 150, 9 (2009), 604–612.
annals of internal medicine 150, 9 (2009), 604–612。
0.80
[24] Oscar Li, Hao Liu, Chaofan Chen, and Cynthia Rudin.
In Thirty-Second AAAI Conference on Artificial Intelligence.
人工知能に関する第3回AAAI会議に参加。
0.54
[25] Scott M Lundberg and Su-In Lee.
[25] Scott M LundbergとSu-In Lee。
0.93
2017. A unified approach to interpreting model predictions.
2017. モデル予測を統一的に解釈するアプローチ。
0.83
In Advances in neural information processing systems.
神経情報処理システムの進歩。
0.61
4765–4774.
4765–4774.
0.71
[26] Robert L McNamara, Kevin F Kennedy, David J Cohen, Deborah B Diercks, Mauro Moscucci, Stephen Ramee, Tracy Y Wang, Traci Connolly, and John A Spertus.
Robert L McNamara, Kevin F Kennedy, David J Cohen, Deborah B Diercks, Mauro Moscucci, Stephen Ramee, Tracy Y Wang, Traci Connolly, John A Spertus。
0.72
2016. Predicting in-hospital mortality in patients with acute myocardial infarction.
2016. 急性心筋梗塞患者における病院内死亡率の予測
0.82
Journal of the American College of Cardiology 68, 6 (2016), 626–635.
Journal of the American College of Cardiology 68, 6 (2016), 626–635。
0.85
[27] David Alvarez Melis and Tommi Jaakkola.
27] David Alvarez MelisとTommi Jaakkola。
0.72
2018. Towards robust interpretability with self-explaining neural networks.
2018. 自己表現型ニューラルネットワークによる堅牢な解釈性の実現。
0.71
In Advances in Neural Information Processing Systems.
神経情報処理システムの進歩です
0.58
7775–7784.
7775–7784.
0.71
[28] Tim Miller.
ティム・ミラー(Tim Miller)。
0.58
2019. Explanation in artificial intelligence: Insights from the social sciences.
2019. 人工知能における説明:社会科学からの洞察。
0.79
Artificial Intelligence 267 (2019), 1–38.
人工知能267 (2019), 1-38。
0.69
[29] David A Morrow, Elliott M Antman, Lori Parsons, James A de Lemos, Christopher P Cannon, Robert P Giugliano, Carolyn H McCabe, Hal V Barron, and Eugene Braunwald.
1729] David A Morrow, Elliott M Antman, Lori Parsons, James A de Lemos, Christopher P Cannon, Robert P Giugliano, Carolyn H McCabe, Hal V Barron, Eugene Braunwald。
0.76
2001. Application of the TIMI risk score for ST-elevation MI in the National Registry of Myocardial Infarction 3.
2001. 心筋梗塞全国登録簿におけるST上昇MIに対するTIMIリスクスコアの応用
0.72
Jama 286, 11 (2001), 1356–1359.
Jama 286, 11 (2001), 1356–1359。
0.86
[30] Paul D. Myers, Wei Huang, Fred Anderson, and Collin M. Stultz.
30] Paul D. Myers、Wei Huang、Fred Anderson、Collin M. Stultz。
0.75
2019. Choosing Clinical Variables for Risk Stratification Post-Acute Coronary Syndrome.
2019. 急性冠症候群のリスク階層化のための臨床変数の選択
0.74
Scientific Reports 9, 1 (2019), 14631. https://doi.org/10.1 038/s41598-019-50933 -3 [31] Paul D Myers, Kenney Ng, Kristen Severson, Uri Kartoun, Wangzhi Dai, Wei Huang, Frederick A Anderson, and Collin M Stultz.
Scientific Reports 9, 1 (2019), 14631.https://doi.or g/10.1038/s41598-019 -50933-3 [31] Paul D Myers, Kenney Ng, Kristen Severson, Uri Kartoun, Wangzhi Dai, Wei Huang, Frederick A Anderson, Collin M Stultz
0.86
2020. Identifying unreliable predictions in clinical risk models.
2020. 臨床リスクモデルにおける信頼できない予測の特定
0.77
NPJ digital medicine 3, 1 (2020), 1–8.
NPJ Digital Medicine 3, 1 (2020), 1–8。
0.83
[32] Radford M Neal and Geoffrey E Hinton.
32] Radford M NealとGeoffrey E Hinton。
0.67
1998. A view of the EM algorithm that justifies incremental, sparse, and other variants.
2019. Regularizing Black-box Models for Improved Interpretability.
2019. 解釈性向上のためのブラックボックスモデルを正規化。
0.69
arXiv preprint arXiv:1902.06787 (2019).
arXiv preprint arXiv:1902.06787 (2019)
0.83
[34] Sushravya Raghunath, Alvaro E Ulloa Cerna, Linyuan Jing, Joshua Stough, Dustin N Hartzel, Joseph B Leader, H Lester Kirchner, Martin C Stumpe, Ashraf Hafez, Arun Nemani, et al 2020.
34] Sushravya Raghunath, Alvaro E Ulloa Cerna, Linyuan Jing, Joshua Stough, Dustin N Hartzel, Joseph B Leader, H Lester Kirchner, Martin C Stumpe, Ashraf Hafez, Arun Nemani, et al 2020。
0.82
Prediction of mortality from 12-lead electrocardiogram voltage data using a deep neural network.
ディープニューラルネットワークを用いた12誘導心電図電圧データによる死亡予測
0.81
Nature Medicine (2020), 1–6.
自然医学(2020年)、1-6。
0.69
[35] Carl Edward Rasmussen.
カール・エドワード・ラスムセン(Carl Edward Rasmussen)
0.62
2003. Gaussian processes in machine learning.
2003. 機械学習におけるガウス過程。
0.79
In Summer School on Machine Learning.
サマースクールで機械学習を学ぶ。
0.67
Springer, 63–71.
スプリンガー63-71。
0.45
[36] Danilo Jimenez Rezende, Shakir Mohamed, and Daan Wierstra.
2014. Stochastic backpropagation and approximate inference in deep generative models.
2014. 深部生成モデルにおける確率的バックプロパゲーションと近似推論
0.77
In Proceedings of the 31st International Conference on International Conference on Machine Learning-Volume 32.
第31回「機械学習に関する国際会議」の開催にあたって
0.64
II–1278. [37] Matthew T Roe, Anita Y Chen, Laine Thomas, Tracy Y Wang, Karen P Alexander, Bradley G Hammill, W Brian Gibler, E Magnus Ohman, and Eric D Peterson.
1278年。 Matthew T Roe氏、Anita Y Chen氏、Laine Thomas氏、Tracy Y Wang氏、Karen P Alexander氏、Bradley G Hammill氏、W Brian Gibler氏、E Magnus Ohman氏、Eric D Peterson氏。
0.65
2011. Predicting long-term mortality in older patients after non–ST-segment elevation myocardial infarction: the CRUSADE long-term mortality model and risk score.
[38] Kiichi Sagawa, Reidar K Lie, and Jochen Schaefer.
[38] 佐川喜一、レイダー・k・リー、ヨッヘン・シェーファー
0.47
1990. Translation of Otto Frank’s paper “Die Grundform des arteriellen Pulses” zeitschrift für biologie 37:
1990. オットー・フランクの論文 "die grundform des arteriellen pulses" zeitschrift für biologie 37:
0.76
英語（論文から抽出）
日本語訳
スコア
Consider the data likelihood term alone:
データ可能性の用語だけを考えると
0.67
= log 𝑝(𝜙) + log 𝑝(𝜓) + log 𝑝(𝑥 𝑁 1
log p(φ) + log p(*) + log p(x N 1) です。
0.88
1 |𝜙,𝜓). , 𝑦𝑁
1 |𝜙,𝜓). , 𝑦𝑁
0.91
(11) (12) (13)
(11) (12) (13)
0.85
ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA
ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA
0.96
because data points are iid.
データポイントは iid だからです
0.83
Then, considering a single term of this sum:
そして、この合計の1つの項を考えると
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Learning to Predict with Supporting Evidence A DERIVATION OF LOWER BOUND FOR VARIATIONAL EM We lower bound the joint log likelihood of data and model parameters: log 𝑝(𝜙,𝜓, D) = log 𝑝(𝜙,𝜓, 𝑥 𝑁 1 ) , 𝑦𝑁 1 𝑁∑︁ log 𝑝(𝑥 𝑁 1 |𝜙,𝜓) = log 𝑝(𝑥𝑖, 𝑦𝑖|𝜙,𝜓), , 𝑦𝑁 1 𝑖=1 (cid:16)∫ 𝑝(𝜋, 𝑦𝑖, 𝑧, 𝑥𝑖|𝜙,𝜓)𝑑𝜋𝑑𝑧(cid:17) log 𝑝(𝑥𝑖, 𝑦𝑖|𝜙,𝜓) (cid:16)∫ 𝑞(𝜋, 𝑧) 𝑞(𝜋, 𝑧) 𝑝(𝜋, 𝑦𝑖, 𝑧, 𝑥𝑖|𝜙,𝜓)𝑑𝜋𝑑𝑧(cid:17) = log ∫ (cid:17)𝑑𝜋𝑑𝑧 (cid:16) 𝑝(𝜋, 𝑦𝑖, 𝑧, 𝑥𝑖|𝜙,𝜓) = log (cid:104) log 𝑝(𝜋, 𝑦𝑖, 𝑧, 𝑥𝑖|𝜙,𝜓)(cid:105) + 𝐻(𝑞), 𝑞(𝜋, 𝑧) log ≥ 𝑞(𝜋, 𝑧) = E𝜋,𝑧∼𝑞(𝜋,𝑧)
Learning to Predict with Supporting Evidence A DERIVATION OF LOWER BOUND FOR VARIATIONAL EM We lower bound the joint log likelihood of data and model parameters: log 𝑝(𝜙,𝜓, D) = log 𝑝(𝜙,𝜓, 𝑥 𝑁 1 ) , 𝑦𝑁 1 𝑁∑︁ log 𝑝(𝑥 𝑁 1 |𝜙,𝜓) = log 𝑝(𝑥𝑖, 𝑦𝑖|𝜙,𝜓), , 𝑦𝑁 1 𝑖=1 (cid:16)∫ 𝑝(𝜋, 𝑦𝑖, 𝑧, 𝑥𝑖|𝜙,𝜓)𝑑𝜋𝑑𝑧(cid:17) log 𝑝(𝑥𝑖, 𝑦𝑖|𝜙,𝜓) (cid:16)∫ 𝑞(𝜋, 𝑧) 𝑞(𝜋, 𝑧) 𝑝(𝜋, 𝑦𝑖, 𝑧, 𝑥𝑖|𝜙,𝜓)𝑑𝜋𝑑𝑧(cid:17) = log ∫ (cid:17)𝑑𝜋𝑑𝑧 (cid:16) 𝑝(𝜋, 𝑦𝑖, 𝑧, 𝑥𝑖|𝜙,𝜓) = log (cid:104) log 𝑝(𝜋, 𝑦𝑖, 𝑧, 𝑥𝑖|𝜙,𝜓)(cid:105) + 𝐻(𝑞), 𝑞(𝜋, 𝑧) log ≥ 𝑞(𝜋, 𝑧) = E𝜋,𝑧∼𝑞(𝜋,𝑧)
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(14) (15) (16) (17) (18) where 𝑞 is some distribution over the latent variables 𝜋, 𝑧, the inequality in (17) comes from Jensen’s inequality and concavity of log, and 𝐻(𝑞) is the entropy of distribution 𝑞.
ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA B ADDITIONAL DETAILS ON RELATED WORK We provide more details comparing LPS to three methods that support predictions with concept-based explanation: • Contextual Explanation Networks [1]: Uses both high dimensional input (e g an image) and a set of labelled attributes for each example in making a predictive decision, with the high-dimensional input used to generate weights for these attributes in the predictor.
ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA B ADDITIONAL DETAILS ON RELATED WORK コンセプトベースの説明で予測をサポートする3つの方法にLPSを比較する詳細を提供します。 • コンテキスト説明ネットワーク [1]:予測器のこれらの属性の重みを生成するために使用される高次元入力(例えば画像)と、予測決定を行う各例のラベル付き属性のセットの両方を使用します。
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In contrast, LPS does not assume that these labelled attributes exist for every example, and instead enforces groundedness of the supporting evidence concepts using a forward model and domain knowledge.
• Self-Explaining Neural Networks [27]: provides explanations for predictions by learning a neural network model that forms predictions as a product of input-dependent concepts and weighting terms for these concepts.
The concepts for explanations are learned from data (not constrained by domain understanding) and are interpreted by considering input examples that most characterise them (they do not necessarily have an inherent interpretation).
Furthermore, since SENN uses input examples as prototypes to characterise learned concepts.
さらに、sennは入力例をプロトタイプとして学習概念を特徴付ける。
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With complex, multimodal data, as in our clinical experiment, such examples can be challenging to visualise and understand, unlike LPS concepts, which have a direct interpretation.
C ADDITIONAL INFORMATION FOR EXPERIMENTS We provide further information for experiments.
C ADDITIONAL Information for EXPERIMENTS 実験のためのさらなる情報を提供します。
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C.1 Network Architectures Learnable forward model: The network 𝑓 (𝑧,𝜓) models observed tabular features and the ECG.
c.1 network architectures learnable forward model: the network f (z,ψ) model observed tabular features and the ecg。
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Generating the entire 12 lead ECG is challenging, so we approximate the respective term in the objective function (𝑝(𝑥 (𝑓 )|𝑧,𝜓)) by computing the log probability of the first 500 samples of the first lead.
• A final FC layer produces the mean and variance parameters for the posterior on each 𝑧𝑚, and the Beta distribution concentration parameters for the posterior on 𝜋.
Learning to Predict with Supporting Evidence ACM CHIL ’21, April 8–10, 2021, Virtual Event, USA MAP Inference Network: The MAP network 𝑛(𝑥; 𝜃𝑛) is a neural network with the same architecture as the variational posterior network, except that it directly outputs the MAP estimates of 𝑧 and 𝜋. C.2 Implementation and Training Details We learn MAP parameter estimates for the model by maximising a lower bound on the log evidence.
acm chil ′21, april 8–10, 2021, virtual event, usa map inference network: the map network n(x; θn) is a same architecture with the variational posterior network, but it direct outputs the map estimates of z and π.2 implementation and training details we learn map parameter estimates for the model. (英語) 訳抜け防止モード: 2021年4月8-10日、ACM CHILのエビデンス支援による予測の学習 仮想イベント,USA MAP推論ネットワーク : MAPネットワーク n(x, θn) は変動後ネットワークと同じ構造を持つニューラルネットワークである。 z と π の MAP 推定を直接出力する以外は C.2 の実装と訓練の詳細 我々は,ログエビデンスに対する下位境界を最大化することにより,モデルのMAPパラメータ推定を学習する。
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We approximate the expectation in this lower bound by drawing a single sample from the variational posterior using the reparameterisation trick [18, 36], allowing end-to-end gradient-based training of the parameters 𝜙, the variational posterior parameters 𝜃𝑞 and the forward model parameters 𝜓.
In practice, we use a small number of empirical adjustments: (i) we only maximise the log probability of the first 500 samples of the ECG (to simplify the modelling problem); (ii) for the first 10 epochs of training, we do not use the data likelihood term 𝑝(𝑥|𝑧,𝜓) in the objective, for learning stability.
We use Adam [17] for maximising this lower bound, with a learning rate of 1e-4.
この下限を最大化するためにadam[17]を使用し、学習率は1e-4である。
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Training is for 200 epochs with a batch size of 32.
トレーニングは200エポックで、バッチサイズは32である。
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This yields approximate MAP estimates 𝜙∗,𝜓∗, and variational posterior parameters 𝜃∗ 𝑞.
これにより近似写像推定 φ∗,∗∗ と変分後パラメータ θ∗ q が得られる。
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To learn the MAP inference network 𝑛(𝑥; 𝜃𝑛) → ( ^𝜋, ^𝑧), we train with Adam for 200 epochs, with a learning rate of 1e-3 and a batch size log 𝑝( ^𝜋) + log 𝑝(𝑦𝑖| ^𝜋)+ log 𝑝(^𝑧| ^𝜋, 𝜙∗) + log 𝑝(𝑥𝑖|^𝑧,𝜓∗)(cid:105) .
The objective function is as follows, with a batch size of 𝐾: 𝑖=1 The baseline model has the same architecture as the MAP inference network, except it only outputs the class probability and is trained using a standard binary cross entropy loss.
i=1 ベースラインモデルはMAP推論ネットワークと同じアーキテクチャを持ち、クラス確率のみを出力し、標準的なバイナリクロスエントロピーロスを使用して訓練される。 訳抜け防止モード: 目的関数は以下の通りで、バッチサイズは K : i=1 ベースラインモデルはMAP推論ネットワークと同じアーキテクチャを持つ。 ただし、クラス確率のみを出力し、標準的なバイナリクロスエントロピー損失を使用してトレーニングされる。
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This model is trained for 200 epochs with Adam, with a learning rate of 1e-3 and batch size of 32.
SENN is implemented with the same autoencoder architecture as the LPS variational autoencoder, and uses 5 basis concepts (to enable comparison with LPS).
We examined different learning rate and sparsity parameters on the validation set.
検証セット上で異なる学習率とスパーシティパラメータを検討した。
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Choice of architectures and hyperparameters: For the learnable forward model, we based our architecture on standard upsampling architectures used in deconvolutional networks.
We investigated shallower and deeper architectures and decided on this architecture based on reconstruction performance.
より浅層・深層構造を調査し, 復元性能に基づいて検討した。
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The baseline, MAP, and variational posterior networks here using FC layers and 1D CNNs is based on the architecture from [34], with an additional residual network structure for the backbone of the network to extract ECG features.