相关论文: Learning $\mathsf{AC}^0$ Under Graphical Models

Unlearning is challenging in generic learning frameworks with the continuous growth and updates of models exhibiting complex inheritance relationships. This paper presents a novel unlearning framework that enables fully parallel unlearning…

In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the…

Distribution shifts on graphs -- the discrepancies in data distribution between training and employing a graph machine learning model -- are ubiquitous and often unavoidable in real-world scenarios. These shifts may severely deteriorate…

We propose a Bayesian approximate inference method for learning the dependence structure of a Gaussian graphical model. Using pseudo-likelihood, we derive an analytical expression to approximate the marginal likelihood for an arbitrary…

Learning the directed acyclic graph (DAG) structure of a Bayesian network from observational data is a notoriously difficult problem for which many hardness results are known. In this paper we propose a provably polynomial-time algorithm…

Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified…

We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let $f$ be the density function of an arbitrary univariate distribution,…

In the last decade, the approximate vanishing ideal and its basis construction algorithms have been extensively studied in computer algebra and machine learning as a general model to reconstruct the algebraic variety on which noisy data…

Modern machine learning techniques are successfully being adapted to data modeled as graphs. However, many real-world graphs are typically very large and do not fit in memory, often making the problem of training machine learning models on…

Counting and sampling directed acyclic graphs from a Markov equivalence class are fundamental tasks in graphical causal analysis. In this paper we show that these tasks can be performed in polynomial time, solving a long-standing open…

Inverse problems correspond to a certain type of optimization problems formulated over appropriate input distributions. Recently, there has been a growing interest in understanding the computational hardness of these optimization problems,…

Quantum neural networks are expected to be a promising application in near-term quantum computing, but face challenges such as vanishing gradients during optimization and limited expressibility by a limited number of qubits and shallow…

In deep learning, a central issue is to understand how neural networks efficiently learn high-dimensional features. To this end, we explore the gradient descent learning of a general Gaussian Multi-index model…

Sample complexity bounds are a common performance metric in the Reinforcement Learning literature. In the discounted cost, infinite horizon setting, all of the known bounds have a factor that is a polynomial in $1/(1-\gamma)$, where $\gamma…

Structure learning of Gaussian graphical models is an extensively studied problem in the classical multivariate setting where the sample size n is larger than the number of random variables p, as well as in the more challenging setting when…

This work examines the problem of graph learning over a diffusion network when data can be collected from a limited portion of the network (partial observability). The main question is to establish technical guarantees of consistent…

We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…

We study the problem of learning a binary classifier on the vertices of a graph. In particular, we consider classifiers given by monophonic halfspaces, partitions of the vertices that are convex in a certain abstract sense. Monophonic…

The works presented in this habilitation concern the algorithmics of polynomials. This is a central topic in computer algebra, with numerous applications both within and outside the field - cryptography, error-correcting codes, etc. For…

This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of…