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We introduce here a rewrite system in the group of unimodular matrices, \emph{i.e.}, matrices with integer entries and with determinant equal to $\pm 1$. We use this rewrite system to precisely characterize the mechanism of the Gaussian…
We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global…
Motivated by the recent empirical successes of deep generative models, we study the computational complexity of the following unsupervised learning problem. For an unknown neural network $F:\mathbb{R}^d\to\mathbb{R}^{d'}$, let $D$ be the…
In the context of high-dimensional Gaussian linear regression for ordered variables, we study the variable selection procedure via the minimization of the penalized least-squares criterion. We focus on model selection where the penalty…
This paper investigates the joint compression problem of a vector Gaussian source, where an individual distortion constraint is imposed on each source component. It is known that the rate-distortion function (RDF) is lower-bounded by the…
We prove that the finite-difference based derivative-free descent (FD-DFD) methods have a capability to find the global minima for a class of multiple minima problems. Our main result shows that, for a class of multiple minima objectives…
We study gap-dependent performance guarantees for nearly minimax-optimal algorithms in reinforcement learning with linear function approximation. While prior works have established gap-dependent regret bounds in this setting, existing…
Given a fixed matrix, the problem of column subset selection requests a column submatrix that has favorable spectral properties. Most research from the algorithms and numerical linear algebra communities focuses on a variant called…
We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model…
Optimization tasks over relational data, such as clustering, often suffer from the prohibitive cost of join operations, which are necessary to access the full dataset. While geometric data structures like BBD trees yield fast approximation…
This paper presents an advanced Federated Learning (FL) framework for forecasting complex spatiotemporal data, improving upon recent state-of-the-art models. In the proposed approach, the original Gated Recurrent Unit (GRU) module within…
We give structured proofs for five mathematical propositions governing synchronous peer-to-peer computation on a finite grid graph embedded in $\mathbb{Z}^2$. Proposition 1 gives three lower bounds: a transport-work bound $\sum_i a_i \ell_i…
We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For…
Exponential family models, generalized linear models (GLMs), generalized linear mixed models (GLMMs) and generalized additive models (GAMs) are widely used methods in statistics. However, many scientific applications necessitate constraints…
Sequence generators obtained by linear recursions over the two-element field $\mathbb{F}_2$, i.e., $\mathbb{F}_2$-linear generators, are widely used as pseudorandom number generators. For example, the Mersenne Twister MT19937 is one of the…
We study the combinatorial contracting problem of D\"utting et al. [FOCS '21], in which a principal seeks to incentivize an agent to take a set of costly actions. In their model, there is a binary outcome (the agent can succeed or fail),…
This paper studies the limitations of the generic approaches to solving cryptographic problems in classical and quantum settings in various models. - In the classical generic group model (GGM), we find simple alternative proofs for the…
The Shortest Lattice Vector (SLV) problem is in general hard to solve, except for special cases (such as root lattices and lattices for which an obtuse superbase is known). In this paper, we present a new class of SLV problems that can be…
Federated Learning (FL) is an emerging framework for distributed processing of large data volumes by edge devices subject to limited communication bandwidths, heterogeneity in data distributions and computational resources, as well as…
In this paper, we present FPT-algorithms for special cases of the shortest lattice vector, integer linear programming, and simplex width computation problems, when matrices included in the problems' formulations are near square. The…