arXiv subjects

Saharon Rosset

Publications and source records attributed to Saharon Rosset.

At least 19 recordsLinked to original sources

arXiv2026

Selecting Informative Conformal Prediction Sets with an Optimized FCR-Controlled Approach

Conformal methods provide prediction sets for outcomes with confidence guarantees. We study their use in a selective inference setting, where inference is performed only when the prediction set is informative. The analyst may consider as informative, for example, cases with prediction sets that are sufficiently small, exclude null values, or satisfy other appropriate monotone constraints. Because inference is typically restricted to informative cases in practical applications, accounting for the resulting selection bias is crucial to maintaining false coverage rate (FCR) control. A general framework for constructing such informative conformal prediction sets while controlling the FCR on the selected sample was suggested in Gazin et al. (2025). In this work we focus on oracle-guided procedures. We derive the optimal decision policy under a suitable power objective in the oracle setting where the probability of belonging to each prediction set can be computed. In practice, of course, only estimated probabilities are available. We therefore introduce a calibration procedure that adjusts the oracle policy to maintain finite sample FCR control. We show that this approach can achieve substantially higher power than available alternatives. We demonstrate the effectiveness of our new methods for classification outcomes on both real and simulated data.

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arXiv2025

Improving Multi-Class Calibration through Normalization-Aware Isotonic Techniques

Accurate and reliable probability predictions are essential for multi-class supervised learning tasks, where well-calibrated models enable rational decision-making. While isotonic regression has proven effective for binary calibration, its extension to multi-class problems via one-vs-rest calibration produced suboptimal results when compared to parametric methods, limiting its practical adoption. In this work, we propose novel isotonic normalization-aware techniques for multiclass calibration, grounded in natural and intuitive assumptions expected by practitioners. Unlike prior approaches, our methods inherently account for probability normalization by either incorporating normalization directly into the optimization process (NA-FIR) or modeling the problem as a cumulative bivariate isotonic regression (SCIR). Empirical evaluation on a variety of text and image classification datasets across different model architectures reveals that our approach consistently improves negative log-likelihood (NLL) and expected calibration error (ECE) metrics.

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arXiv2025

The Bottom-Up Approach for Powerful Testing with FWER Control

We seek to design novel multiple testing procedures, which take into account a relevant notion of ''power'' or true discovery on the one hand, and allow computationally efficient test design and application on the other. Towards this end we characterize the optimal procedures that strongly control the family-wise error rate, for a range of power objectives measuring the success of multiple testing procedures in making true individual discoveries, and under a reasonable set of assumptions. While we cannot generally find these optimal solutions in practice, we propose the bottom-up approach, which constructs consonant closed testing procedures, while taking into account the overall power objective in designing the tests on every level of the closed testing hierarchy. This leads to a general recipe, yielding novel procedures which are computationally practical and demonstrate substantially improved power in both simulations and a real data study, compared to existing procedures.

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arXiv2025

MMbeddings: Parameter-Efficient, Low-Overfitting Probabilistic Embeddings Inspired by Nonlinear Mixed Models

We present MMbeddings, a probabilistic embedding approach that reinterprets categorical embeddings through the lens of nonlinear mixed models, effectively bridging classical statistical theory with modern deep learning. By treating embeddings as latent random effects within a variational autoencoder framework, our method substantially decreases the number of parameters -- from the conventional embedding approach of cardinality $\times$ embedding dimension, which quickly becomes infeasible with large cardinalities, to a significantly smaller, cardinality-independent number determined primarily by the encoder architecture. This reduction dramatically mitigates overfitting and computational burden in high-cardinality settings. Extensive experiments on simulated and real datasets, encompassing collaborative filtering and tabular regression tasks using varied architectures, demonstrate that MMbeddings consistently outperforms traditional embeddings, underscoring its potential across diverse machine learning applications.

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arXiv2025

Cross Validation for Correlated Data in Regression and Classification Models, with Applications to Deep Learning

We present a methodology for model evaluation and selection where the sampling mechanism violates the i.i.d. assumption. Our methodology involves a formulation of the bias between the standard Cross-Validation (CV) estimator and the mean generalization error, denoted by $w_{cv}$, and practical data-based procedures to estimate this term. This concept was introduced in the literature only in the context of a linear model with squared error loss as the criterion for prediction performance. Our proposed bias-corrected CV estimator, $\text{CV}_c=\text{CV}+w_{cv}$, can be applied to any learning model, including deep neural networks, and to a wide class of criteria for prediction performance in regression and classification tasks. We demonstrate the applicability of the proposed methodology in various scenarios where the data contains complex correlation structures (such as clustered and spatial relationships) with synthetic data and real-world datasets, providing evidence that the estimator $\text{CV}_c$ is better than the standard CV estimator. This paper is an expanded version of our published conference paper.

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arXiv2024

Integrating Random Effects in Variational Autoencoders for Dimensionality Reduction of Correlated Data

Variational Autoencoders (VAE) are widely used for dimensionality reduction of large-scale tabular and image datasets, under the assumption of independence between data observations. In practice, however, datasets are often correlated, with typical sources of correlation including spatial, temporal and clustering structures. Inspired by the literature on linear mixed models (LMM), we propose LMMVAE -- a novel model which separates the classic VAE latent model into fixed and random parts. While the fixed part assumes the latent variables are independent as usual, the random part consists of latent variables which are correlated between similar clusters in the data such as nearby locations or successive measurements. The classic VAE architecture and loss are modified accordingly. LMMVAE is shown to improve squared reconstruction error and negative likelihood loss significantly on unseen data, with simulated as well as real datasets from various applications and correlation scenarios. It also shows improvement in the performance of downstream tasks such as supervised classification on the learned representations.

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arXiv2023

Mixed Semi-Supervised Generalized-Linear-Regression with Applications to Deep-Learning and Interpolators

We present a methodology for using unlabeled data to design semi-supervised learning (SSL) methods that improve the predictive performance of supervised learning for regression tasks. The main idea is to design different mechanisms for integrating the unlabeled data, and include in each of them a mixing parameter $\alpha$, controlling the weight given to the unlabeled data. Focusing on Generalized Linear Models (GLM) and linear interpolators classes of models, we analyze the characteristics of different mixing mechanisms, and prove that it is consistently beneficial to integrate the unlabeled data with some nonzero mixing ratio $\alpha>0$, in terms of predictive performance. Moreover, we provide a rigorous framework to estimate the best mixing ratio where mixed-SSL delivers the best predictive performance, while using the labeled and unlabeled data on hand. The effectiveness of our methodology in delivering substantial improvement compared to the standard supervised models, in a variety of settings, is demonstrated empirically through extensive simulation, providing empirical support for our theoretical analysis. We also demonstrate the applicability of our methodology (with some heuristic modifications) to improve more complex models, such as deep neural networks, in real-world regression tasks

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arXiv2022

Inference with approximate local false discovery rates

Efron's two-group model is widely used in large scale multiple testing. This model assumes that test statistics are mutually independent, however in realistic settings they are typically dependent, and taking the dependence into account can boost power. The general two-group model takes the dependence between the test statistics into account. Optimal policies in the general two-group model require calculation, for each hypothesis, of the probability that it is a true null given all test statistics, denoted local false discovery rate (locFDR). Unfortunately, calculating locFDRs under realistic dependence structures can be computationally prohibitive. We propose calculating approximate locFDRs based on a properly defined N-neighborhood for each hypothesis. We prove that by thresholding the approximate locFDRs with a fixed threshold, the marginal false discovery rate is controlled for any dependence structure. Furthermore, we prove that this is the optimal procedure in a restricted class of decision rules, where decision for each hypothesis is only guided by its N-neighborhood. We show through extensive simulations that our proposed method achieves substantial power gains compared to alternative practical approaches, while maintaining conceptual simplicity and computational feasibility. We demonstrate the utility of our method on a genome wide association study of height.

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arXiv2022

Optimal multiple testing and design in clinical trials

A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a false null hypothesis subject to the constraint of type I error. When there is more than one test, such as in clinical trials with multiple endpoints, the issues of optimal design and optimal procedures become more complex. In this paper we address the question of how such optimal tests should be defined and how they can be found. We review different notions of power and how they relate to study goals, and also consider the requirements of type I error control and the nature of the procedures. This leads us to an explicit optimization problem with objective and constraints which describe its specific desiderata. We present a complete solution for deriving optimal procedures for two hypotheses, which have desired monotonicity properties, and are computationally simple. For some of the optimization formulations this yields optimal procedures that are identical to existing procedures, such as Hommel's procedure or the procedure of Bittman et al. (2009), while for others it yields completely novel and more powerful policies than existing ones. We demonstrate the nature of our novel policies and their improved power extensively in simulation and on the APEX study (Cohen et al., 2016).

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arXiv2022

Integrating Random Effects in Deep Neural Networks

Modern approaches to supervised learning like deep neural networks (DNNs) typically implicitly assume that observed responses are statistically independent. In contrast, correlated data are prevalent in real-life large-scale applications, with typical sources of correlation including spatial, temporal and clustering structures. These correlations are either ignored by DNNs, or ad-hoc solutions are developed for specific use cases. We propose to use the mixed models framework to handle correlated data in DNNs. By treating the effects underlying the correlation structure as random effects, mixed models are able to avoid overfitted parameter estimates and ultimately yield better predictive performance. The key to combining mixed models and DNNs is using the Gaussian negative log-likelihood (NLL) as a natural loss function that is minimized with DNN machinery including stochastic gradient descent (SGD). Since NLL does not decompose like standard DNN loss functions, the use of SGD with NLL presents some theoretical and implementation challenges, which we address. Our approach which we call LMMNN is demonstrated to improve performance over natural competitors in various correlation scenarios on diverse simulated and real datasets. Our focus is on a regression setting and tabular datasets, but we also show some results for classification. Our code is available at https://github.com/gsimchoni/lmmnn.

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arXiv2022

Semi-Supervised Empirical Risk Minimization: Using unlabeled data to improve prediction

We present a general methodology for using unlabeled data to design semi supervised learning (SSL) variants of the Empirical Risk Minimization (ERM) learning process. Focusing on generalized linear regression, we analyze of the effectiveness of our SSL approach in improving prediction performance. The key ideas are carefully considering the null model as a competitor, and utilizing the unlabeled data to determine signal-noise combinations where SSL outperforms both supervised learning and the null model. We then use SSL in an adaptive manner based on estimation of the signal and noise. In the special case of linear regression with Gaussian covariates, we prove that the non-adaptive SSL version is in fact not capable of improving on both the supervised estimator and the null model simultaneously, beyond a negligible O(1/n) term. On the other hand, the adaptive model presented in this work, can achieve a substantial improvement over both competitors simultaneously, under a variety of settings. This is shown empirically through extensive simulations, and extended to other scenarios, such as non-Gaussian covariates, misspecified linear regression, or generalized linear regression with non-linear link functions.

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arXiv2021

Trees-Based Models for Correlated Data

This paper presents a new approach for trees-based regression, such as simple regression tree, random forest and gradient boosting, in settings involving correlated data. We show the problems that arise when implementing standard trees-based regression models, which ignore the correlation structure. Our new approach explicitly takes the correlation structure into account in the splitting criterion, stopping rules and fitted values in the leaves, which induces some major modifications of standard methodology. The superiority of our new approach over trees-based models that do not account for the correlation is supported by simulation experiments and real data analyses.

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arXiv2021

Resampling Methods for Detecting Anisotropic Correlation Structure

This paper proposes parametric and non-parametric hypothesis testing algorithms for detecting anisotropy -- rotational variance of the covariance function in random fields. Both algorithms are based on resampling mechanisms, which enable avoiding relying on asymptotic assumptions, as is common in previous algorithms. The algorithms' performance is illustrated numerically in simulation experiments and on real datasets representing a variety of potential challenges.

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arXiv2020

Surprises in High-Dimensional Ridgeless Least Squares Interpolation

Interpolators -- estimators that achieve zero training error -- have attracted growing attention in machine learning, mainly because state-of-the art neural networks appear to be models of this type. In this paper, we study minimum $\ell_2$ norm ("ridgeless") interpolation in high-dimensional least squares regression. We consider two different models for the feature distribution: a linear model, where the feature vectors $x_i \in {\mathbb R}^p$ are obtained by applying a linear transform to a vector of i.i.d. entries, $x_i = Σ^{1/2} z_i$ (with $z_i \in {\mathbb R}^p$); and a nonlinear model, where the feature vectors are obtained by passing the input through a random one-layer neural network, $x_i = φ(W z_i)$ (with $z_i \in {\mathbb R}^d$, $W \in {\mathbb R}^{p \times d}$ a matrix of i.i.d. entries, and $φ$ an activation function acting componentwise on $W z_i$). We recover -- in a precise quantitative way -- several phenomena that have been observed in large-scale neural networks and kernel machines, including the "double descent" behavior of the prediction risk, and the potential benefits of overparametrization.

math.ST↗

arXiv2020

Optimal and Maximin Procedures for Multiple Testing Problems

Multiple testing problems are a staple of modern statistical analysis. The fundamental objective of multiple testing procedures is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to controlling an overall measure of false discovery, like family-wise error rate (FWER) or false discovery rate (FDR). In this paper we formulate multiple testing of simple hypotheses as an infinite-dimensional optimization problem, seeking the most powerful rejection policy which guarantees strong control of the selected measure. In that sense, our approach is a generalization of the optimal Neyman-Pearson test for a single hypothesis. We show that for exchangeable hypotheses, for both FWER and FDR and relevant notions of power, these problems can be formulated as infinite linear programs and can in principle be solved for any number of hypotheses. We also characterize maximin rules for complex alternatives, and demonstrate that such rules can be found in practice, leading to improved practical procedures compared to existing alternatives. We derive explicit optimal tests for FWER or FDR control for three independent normal means. We find that the power gain over natural competitors is substantial in all settings examined. Finally, we apply our optimal maximin rule to subgroup analyses in systematic reviews from the Cochrane library, leading to an increase in the number of findings while guaranteeing strong FWER control against the one sided alternative.

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arXiv2020

Optimal control of false discovery criteria in the two-group model

The highly influential two-group model in testing a large number of statistical hypotheses assumes that the test statistics are drawn independently from a mixture of a high probability null distribution and a low probability alternative. Optimal control of the marginal false discovery rate (mFDR), in the sense that it provides maximal power (expected true discoveries) subject to mFDR control, is known to be achieved by thresholding the local false discovery rate (locFDR), i.e., the probability of the hypothesis being null given the set of test statistics, with a fixed threshold. We address the challenge of controlling optimally the popular false discovery rate (FDR) or positive FDR (pFDR) rather than mFDR in the general two-group model, which also allows for dependence between the test statistics. These criteria are less conservative than the mFDR criterion, so they make more rejections in expectation. We derive their optimal multiple testing (OMT) policies, which turn out to be thresholding the locFDR with a threshold that is a function of the entire set of statistics. We develop an efficient algorithm for finding these policies, and use it for problems with thousands of hypotheses. We illustrate these procedures on gene expression studies.

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arXiv2020

Cross-Validation for Correlated Data

K-fold cross-validation (CV) with squared error loss is widely used for evaluating predictive models, especially when strong distributional assumptions cannot be taken. However, CV with squared error loss is not free from distributional assumptions, in particular in cases involving non-i.i.d. data. This paper analyzes CV for correlated data. We present a criterion for suitability of standard CV in presence of correlations. When this criterion does not hold, we introduce a bias corrected cross-validation estimator which we term $CV_c,$ that yields an unbiased estimate of prediction error in many settings where standard CV is invalid. We also demonstrate our results numerically, and find that introducing our correction substantially improves both, model evaluation and model selection in simulations and real data studies.

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arXiv2019

Capturing Between-Tasks Covariance and Similarities Using Multivariate Linear Mixed Models

We consider the problem of predicting several response variables using the same set of explanatory variables. This setting naturally induces a group structure over the coefficient matrix, in which every explanatory variable corresponds to a set of related coefficients. Most of the existing methods that utilize this group formation assume that the similarities between related coefficients arise solely through a joint sparsity structure. In this paper, we propose a procedure for constructing an estimator of a multivariate regression coefficient matrix that directly models and captures the within-group similarities, by employing a multivariate linear mixed model formulation, with a joint estimation of covariance matrices for coefficients and errors via penalized likelihood. Our approach, which we term Multivariate random Regression with Covariance Estimation (MrRCE) encourages structured similarity in parameters, in which coefficients for the same variable in related tasks sharing the same sign and similar magnitude. We illustrate the benefits of our approach in synthetic and real examples, and show that the proposed method outperforms natural competitors and alternative estimators under several model settings.

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