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We present a method for computing exact reachable sets for deep neural networks with rectified linear unit (ReLU) activation. Our method is well-suited for use in rigorous safety analysis of robotic perception and control systems with deep…

Random probabilities are a key component to many nonparametric methods in Statistics and Machine Learning. To quantify comparisons between different laws of random probabilities several works are starting to use the elegant Wasserstein over…

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

In this Letter we propose a new method to infer the topology of the interaction network in pairwise models with Ising variables. By using the pseudolikelihood method (PLM) at high temperature, it is generally possible to distinguish between…

We study supervised learning problems that have significant effects on individuals from two demographic groups, and we seek predictors that are fair with respect to a group fairness criterion such as statistical parity (SP). A predictor is…

To avoid specification of the error distribution in a regression model, we propose a general nonparametric scale mixture model for the error distribution. For fitting such mixtures, the predictive recursion method is a simple and…

This paper introduces scalable, sampling-based algorithms that optimize trained neural networks with ReLU activations. We first propose an iterative algorithm that takes advantage of the piecewise linear structure of ReLU neural networks…

Integer linear programming (ILP) is an elegant approach to solve linear optimization problems, naturally described using integer decision variables. Within the context of physics-inspired machine learning applied to chemistry, we…

We propose a new algorithm to learn the network of the interactions of pairwise Ising models. The algorithm is based on the pseudo-likelihood method (PLM), that has already been proven to efficiently solve the problem in a large variety of…

This short study presents an opportunistic approach to a (more) reliable validation method for prediction uncertainty average calibration. Considering that variance-based calibration metrics (ZMS, NLL, RCE...) are quite sensitive to the…

We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple…

We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum,…

Credal sets, i.e., closed convex sets of probability measures, provide a natural framework to represent aleatoric and epistemic uncertainty in machine learning. Yet how to quantify these two types of uncertainty for a given credal set,…

Valid statistical inference is challenging when the sample is subject to unknown selection bias. Data integration can be used to correct for selection bias when we have a parallel probability sample from the same population with some common…

Integer linear programs (ILPs) are commonly employed to model diverse practical problems such as scheduling and planning. Recently, machine learning techniques have been utilized to solve ILPs. A straightforward idea is to train a model via…

Measuring divergence between two distributions is essential in machine learning and statistics and has various applications including binary classification, change point detection, and two-sample test. Furthermore, in the era of big data,…

Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problem related to these models is that the integrals involved in the likelihood function cannot be solved…

Invariant risk minimization (IRM) (Arjovsky et al., 2019) is a recently proposed framework designed for learning predictors that are invariant to spurious correlations across different training environments. Yet, despite its theoretical…

This paper proposes an introspective deep metric learning (IDML) framework for uncertainty-aware comparisons of images. Conventional deep metric learning methods produce confident semantic distances between images regardless of the…

Imputation methods for dealing with incomplete data typically assume that the missingness mechanism is at random (MAR). These methods can also be applied to missing not at random (MNAR) situations, where the user specifies some adjustment…