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This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted…
Interpretable Machine Learning faces a recurring challenge of explaining the predictions made by opaque classifiers such as ensemble models, kernel methods, or neural networks in terms that are understandable to humans. When the model is…
We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…
This paper characterizes the minimax linear estimator of the value of an unknown function at a boundary point of its domain in a Gaussian white noise model under the restriction that the first-order derivative of the unknown function is…
In this paper, our aim is to analyse the generalization capabilities of first-order methods for statistical learning in multiple, different yet related, scenarios including supervised learning, transfer learning, robust learning and…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
This work studies an experimental design problem where {the values of a predictor variable, denoted by $x$}, are to be determined with the goal of estimating a function $m(x)$, which is observed with noise. A linear model is fitted to…
It is a central challenge in deep learning to understand how neural networks learn representations. A leading approach is the Neural Feature Ansatz (NFA) (Radhakrishnan et al. 2024), a conjectured mechanism for how feature learning occurs.…
A key part of any evolutionary algorithm is fitness evaluation. When fitness evaluations are corrupted by noise, as happens in many real-world problems as a consequence of various types of uncertainty, a strategy is needed in order to cope…
Machine learning algorithms typically perform optimization over a class of non-convex functions. In this work, we provide bounds on the fundamental hardness of identifying the global minimizer of a non convex function. Specifically, we…
A trust-region algorithm is presented for finding approximate minimizers of smooth unconstrained functions whose values and derivatives are subject to random noise. It is shown that, under suitable probabilistic assumptions, the new method…
Deep learning classifiers achieve state-of-the-art performance in various risk detection applications. They explore rich semantic representations and are supposed to automatically discover risk behaviors. However, due to the lack of…
Many causal estimands, such as average treatment effects under unconfoundedness, can be written as continuous linear functionals of an unknown regression function. We study a weighting estimator that sets weights by a minimax procedure:…
Estimating location is a central problem in functional data analysis, yet most current estimation procedures either unrealistically assume completely observed trajectories or lack robustness with respect to the many kinds of anomalies one…
This work provides the first finite-time convergence guarantees for linearly constrained stochastic bilevel optimization using only first-order methods, requiring solely gradient information without any Hessian computations or second-order…
In blackbox optimization, evaluation of the objective and constraint functions is time consuming. In some situations, constraint values may be evaluated independently or sequentially. The present work proposes and compares two strategies to…
Quasiminimal structures play an important role in non-elementary categoricity. In this paper we explore possibilities of constructing quasiminimal models of a given first-order theory. We present several constructions with increasing…
In this paper, we provide near-optimal accelerated first-order methods for minimizing a broad class of smooth nonconvex functions that are strictly unimodal on all lines through a minimizer. This function class, which we call the class of…
Causal inference relies on two fundamental assumptions: ignorability and positivity. We study causal inference when the true confounder value can be expressed as a function of the observed data; we call this setting estimation with…
In this paper, we present convergence guarantees for a modified trust-region method designed for minimizing objective functions whose value and gradient and Hessian estimates are computed with noise. These estimates are produced by generic…