CD-split and HPD-split: efficient conformal regions in high dimensions

• URL: http://arxiv.org/abs/2007.12778v3
• Date: Mon, 4 Oct 2021 19:38:50 GMT
• Title: CD-split and HPD-split: efficient conformal regions in high dimensions
• Authors: Rafael Izbicki, Gilson Shimizu, Rafael B. Stern
• Abstract summary: We provide new insights on CD-split by exploring its theoretical properties. We show that CD-split converges to the highest predictive density set and satisfies local variation and conditional validity. We introduce HPD-split, a method of CD-split that requires less tuning, and show that it shares the same theoretical guarantees as CD-split.
• Score: 3.1690891866882236
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Conformal methods create prediction bands that control average coverage assuming solely i.i.d. data. Although the literature has mostly focused on prediction intervals, more general regions can often better represent uncertainty. For instance, a bimodal target is better represented by the union of two intervals. Such prediction regions are obtained by CD-split , which combines the split method and a data-driven partition of the feature space which scales to high dimensions. CD-split however contains many tuning parameters, and their role is not clear. In this paper, we provide new insights on CD-split by exploring its theoretical properties. In particular, we show that CD-split converges asymptotically to the oracle highest predictive density set and satisfies local and asymptotic conditional validity. We also present simulations that show how to tune CD-split. Finally, we introduce HPD-split, a variation of CD-split that requires less tuning, and show that it shares the same theoretical guarantees as CD-split. In a wide variety of our simulations, CD-split and HPD-split have better conditional coverage and yield smaller prediction regions than other methods.

Related papers

• Explaining and Improving Contrastive Decoding by Extrapolating the Probabilities of a Huge and Hypothetical LM [93.8400683020273]
  Contrastive decoding (CD) improves the next-token distribution of a large expert language model (LM) using a small amateur LM. We propose a new unsupervised decoding method called $mathbfA$symptotic $mathbfP$robability $mathbfD$ecoding (APD) APD explicitly extrapolates the probability curves from the LMs of different sizes to infer the probabilities from an infinitely large LM without inducing more inference costs than CD.
  arXiv  Detail & Related papers  (2024-11-03T15:31:44Z)
• Clustering-Based Validation Splits for Model Selection under Domain Shift [0.0]
  It is proposed that the training-validation split should maximise the distribution mismatch between the two sets. A constrained clustering algorithm, which leverages linear programming to control the size, label, and (optionally) group distributions of the splits, is presented.
  arXiv  Detail & Related papers  (2024-05-29T19:21:17Z)
• Toward distortion-aware change detection in realistic scenarios [16.192695430837443]
  We propose a reusable self-supervised framework for bitemporal geometric distortion in CD tasks. The framework is composed of Pretext Representation Pre-training, Bitemporal Image Alignment, and Down-stream Decoder Fine-Tuning. With only single-stage pre-training, the key components of the framework can be reused for assistance in the bitemporal image alignment.
  arXiv  Detail & Related papers  (2024-01-10T13:43:06Z)
• Deep Metric Learning for Unsupervised Remote Sensing Change Detection [60.89777029184023]
  Remote Sensing Change Detection (RS-CD) aims to detect relevant changes from Multi-Temporal Remote Sensing Images (MT-RSIs) The performance of existing RS-CD methods is attributed to training on large annotated datasets. This paper proposes an unsupervised CD method based on deep metric learning that can deal with both of these issues.
  arXiv  Detail & Related papers  (2023-03-16T17:52:45Z)
• Targeted Separation and Convergence with Kernel Discrepancies [61.973643031360254]
  kernel-based discrepancy measures are required to (i) separate a target P from other probability measures or (ii) control weak convergence to P. In this article we derive new sufficient and necessary conditions to ensure (i) and (ii) For MMDs on separable metric spaces, we characterize those kernels that separate Bochner embeddable measures and introduce simple conditions for separating all measures with unbounded kernels.
  arXiv  Detail & Related papers  (2022-09-26T16:41:16Z)
• Revisiting Consistency Regularization for Semi-supervised Change Detection in Remote Sensing Images [60.89777029184023]
  We propose a semi-supervised CD model in which we formulate an unsupervised CD loss in addition to the supervised Cross-Entropy (CE) loss. Experiments conducted on two publicly available CD datasets show that the proposed semi-supervised CD method can reach closer to the performance of supervised CD.
  arXiv  Detail & Related papers  (2022-04-18T17:59:01Z)
• Density-aware Chamfer Distance as a Comprehensive Metric for Point Cloud Completion [90.26652899910019]
  Chamfer Distance (CD) and Earth Mover's Distance (EMD) are two broadly adopted metrics for measuring the similarity between two point sets. We propose a new similarity measure named Density-aware Chamfer Distance (DCD) We show that DCD pays attention to both the overall structure and local details and provides a more reliable evaluation even when CD and contradict each other.
  arXiv  Detail & Related papers  (2021-11-24T18:56:27Z)
• Density Ratio Estimation via Infinitesimal Classification [85.08255198145304]
  We propose DRE-infty, a divide-and-conquer approach to reduce Density ratio estimation (DRE) to a series of easier subproblems. Inspired by Monte Carlo methods, we smoothly interpolate between the two distributions via an infinite continuum of intermediate bridge distributions. We show that our approach performs well on downstream tasks such as mutual information estimation and energy-based modeling on complex, high-dimensional datasets.
  arXiv  Detail & Related papers  (2021-11-22T06:26:29Z)
• Distributional Sliced Embedding Discrepancy for Incomparable Distributions [22.615156512223766]
  Gromov-Wasserstein (GW) distance is a key tool for manifold learning and cross-domain learning. We propose a novel approach for comparing two computation distributions, that hinges on the idea of distributional slicing, embeddings, and on computing the closed-form Wasserstein distance between the sliced distributions.
  arXiv  Detail & Related papers  (2021-06-04T15:11:30Z)

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.