Related papers: Recovery guarantees for polynomial approximation f…
We consider the problem of deriving from experimental data an approximation of an unknown function, whose derivatives also approximate the unknown function derivatives. Solving this problem is useful, for instance, in the context of…
We study a sample complexity vs. conditioning tradeoff in modern signal recovery problems (including sparse recovery, low-rank matrix sensing, covariance estimation, and abstract phase retrieval), where convex optimization problems are…
We study a nonlinear factor model in which observed responses depend on low-rank latent factors through an unknown monotone link function. This setting is challenging and largely underexplored due to severe nonconvexity and identifiability…
We investigate the reconstruction of multivariate functions from samples using sparse recovery techniques. For Square Root Lasso, Orthogonal Matching Pursuit, and Compressive Sampling Matching Pursuit, we demonstrate both theoretically and…
We propose novel necessary and sufficient conditions for a sensing matrix to be "$s$-good" - to allow for exact $\ell_1$-recovery of sparse signals with $s$ nonzero entries when no measurement noise is present. Then we express the error…
We tackle the problem of recovering an unknown signal observed in an ill-posed inverse problem framework. More precisely, we study a procedure commonly used in numerical analysis or image deblurring: minimizing an empirical loss function…
We consider a structured estimation problem where an observed matrix is assumed to be generated as an $s$-sparse linear combination of $N$ given $n\times n$ positive-semidefinite matrices. Recovering the unknown $N$-dimensional and…
Automatically detecting and recovering from failures is an important but challenging problem for autonomous robots. Most of the recent work on learning to plan from demonstrations lacks the ability to detect and recover from errors in the…
We analyze a practical algorithm for sparse PCA on incomplete and noisy data under a general non-random sampling scheme. The algorithm is based on a semidefinite relaxation of the $\ell_1$-regularized PCA problem. We provide theoretical…
This article presents near-optimal guarantees for accurate and robust image recovery from under-sampled noisy measurements using total variation minimization. In particular, we show that from O(slog(N)) nonadaptive linear measurements, an…
Physical models often contain unknown functions and relations. The goal of our work is to answer the question of how one should excite or control a system under consideration in an appropriate way to be able to reconstruct an unknown…
We investigate the problem of learning Bayesian networks in a robust model where an $\epsilon$-fraction of the samples are adversarially corrupted. In this work, we study the fully observable discrete case where the structure of the network…
For various applications, the relations between the dependent and independent variables are highly nonlinear. Consequently, for large scale complex problems, neural networks and regression trees are commonly preferred over linear models…
Conformal unlearning aims to ensure that a trained conformal predictor miscovers data points with specific shared characteristics, such as those from a particular label class, associated with a specific user, or belonging to a defined…
We consider the following learning problem: Given sample pairs of input and output signals generated by an unknown nonlinear system (which is not assumed to be causal or time-invariant), we wish to find a continuous-time recurrent neural…
We formulate sparse support recovery as a salient set identification problem and use information-theoretic analyses to characterize the recovery performance and sample complexity. We consider a very general model where we are not restricted…
Robust model fitting is a core algorithm in a large number of computer vision applications. Solving this problem efficiently for datasets highly contaminated with outliers is, however, still challenging due to the underlying computational…
To solve a new task from minimal experience, it is essential to effectively reuse knowledge from previous tasks, a problem known as meta-learning. Compositional solutions, where common elements of computation are flexibly recombined into…
Reconstructing an image from noisy and incomplete measurements is a central task in several image processing applications. In recent years, state-of-the-art reconstruction methods have been developed based on recent advances in deep…
In supervised learning one wishes to identify a pattern present in a joint distribution $P$, of instances, label pairs, by providing a function $f$ from instances to labels that has low risk $\mathbb{E}_{P}\ell(y,f(x))$. To do so, the…