An interpretable neural network-based non-proportional odds model for ordinal regression

• URL: http://arxiv.org/abs/2303.17823v4
• Date: Mon, 11 Mar 2024 23:28:13 GMT
• Title: An interpretable neural network-based non-proportional odds model for ordinal regression
• Authors: Akifumi Okuno, Kazuharu Harada
• Abstract summary: This study proposes an interpretable neural network-based non-proportional odds model (N$3$POM) for ordinal regression. N$3$POM is different from conventional approaches to ordinal regression with non-proportional models in several ways.
• Score: 3.0277213703725767
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This study proposes an interpretable neural network-based non-proportional odds model (N$^3$POM) for ordinal regression. N$^3$POM is different from conventional approaches to ordinal regression with non-proportional models in several ways: (1) N$^3$POM is defined for both continuous and discrete responses, whereas standard methods typically treat the ordered continuous variables as if they are discrete, (2) instead of estimating response-dependent finite-dimensional coefficients of linear models from discrete responses as is done in conventional approaches, we train a non-linear neural network to serve as a coefficient function. Thanks to the neural network, N$^3$POM offers flexibility while preserving the interpretability of conventional ordinal regression. We establish a sufficient condition under which the predicted conditional cumulative probability locally satisfies the monotonicity constraint over a user-specified region in the covariate space. Additionally, we provide a monotonicity-preserving stochastic (MPS) algorithm for effectively training the neural network. We apply N$^3$POM to several real-world datasets.

Related papers

• Function-Space Regularization in Neural Networks: A Probabilistic Perspective [51.133793272222874]
  We show that we can derive a well-motivated regularization technique that allows explicitly encoding information about desired predictive functions into neural network training. We evaluate the utility of this regularization technique empirically and demonstrate that the proposed method leads to near-perfect semantic shift detection and highly-calibrated predictive uncertainty estimates.
  arXiv  Detail & Related papers  (2023-12-28T17:50:56Z)
• Structured Radial Basis Function Network: Modelling Diversity for Multiple Hypotheses Prediction [51.82628081279621]
  Multi-modal regression is important in forecasting nonstationary processes or with a complex mixture of distributions. A Structured Radial Basis Function Network is presented as an ensemble of multiple hypotheses predictors for regression problems. It is proved that this structured model can efficiently interpolate this tessellation and approximate the multiple hypotheses target distribution.
  arXiv  Detail & Related papers  (2023-09-02T01:27:53Z)
• Learning Theory of Distribution Regression with Neural Networks [6.961253535504979]
  We establish an approximation theory and a learning theory of distribution regression via a fully connected neural network (FNN) In contrast to the classical regression methods, the input variables of distribution regression are probability measures.
  arXiv  Detail & Related papers  (2023-07-07T09:49:11Z)
• A Functional-Space Mean-Field Theory of Partially-Trained Three-Layer Neural Networks [49.870593940818715]
  We study the infinite-width limit of a type of three-layer NN model whose first layer is random and fixed. Our theory accommodates different scaling choices of the model, resulting in two regimes of the MF limit that demonstrate distinctive behaviors.
  arXiv  Detail & Related papers  (2022-10-28T17:26:27Z)
• Learning Low Dimensional State Spaces with Overparameterized Recurrent Neural Nets [57.06026574261203]
  We provide theoretical evidence for learning low-dimensional state spaces, which can also model long-term memory. Experiments corroborate our theory, demonstrating extrapolation via learning low-dimensional state spaces with both linear and non-linear RNNs.
  arXiv  Detail & Related papers  (2022-10-25T14:45:15Z)
• Bagged Polynomial Regression and Neural Networks [0.0]
  Series and dataset regression are able to approximate the same function classes as neural networks. textitbagged regression (BPR) is an attractive alternative to neural networks. BPR performs as well as neural networks in crop classification using satellite data.
  arXiv  Detail & Related papers  (2022-05-17T19:55:56Z)
• DeepBayes -- an estimator for parameter estimation in stochastic nonlinear dynamical models [11.917949887615567]
  We propose DeepBayes estimators that leverage the power of deep recurrent neural networks in learning an estimator. The deep recurrent neural network architectures can be trained offline and ensure significant time savings during inference. We demonstrate the applicability of our proposed method on different example models and perform detailed comparisons with state-of-the-art approaches.
  arXiv  Detail & Related papers  (2022-05-04T18:12:17Z)
• Regularized Sequential Latent Variable Models with Adversarial Neural Networks [33.74611654607262]
  We will present different ways of using high level latent random variables in RNN to model the variability in the sequential data. We will explore possible ways of using adversarial method to train a variational RNN model.
  arXiv  Detail & Related papers  (2021-08-10T08:05:14Z)
• Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach [144.21892195917758]
  We study estimation in a class of generalized Structural equation models (SEMs) We formulate the linear operator equation as a min-max game, where both players are parameterized by neural networks (NNs), and learn the parameters of these neural networks using a gradient descent. For the first time we provide a tractable estimation procedure for SEMs based on NNs with provable convergence and without the need for sample splitting.
  arXiv  Detail & Related papers  (2020-07-02T17:55:47Z)
• Multipole Graph Neural Operator for Parametric Partial Differential Equations [57.90284928158383]
  One of the main challenges in using deep learning-based methods for simulating physical systems is formulating physics-based data. We propose a novel multi-level graph neural network framework that captures interaction at all ranges with only linear complexity. Experiments confirm our multi-graph network learns discretization-invariant solution operators to PDEs and can be evaluated in linear time.
  arXiv  Detail & Related papers  (2020-06-16T21:56:22Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.