Publications associées à Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets

On distributional autoregression and iterated transportation

We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of Double-struck capital R. An order-1 autoregressive model in this context is to be understood as a Markov chain, where ...

Wiley2024

K3 surfaces, cyclotomic polynomials and orthogonal groups

Eva Bayer Fluckiger

Let X be a complex projective K3 surface and let T-X be its transcendental lattice; the characteristic polynomials of isometries of T-X induced by automorphisms of X are powers of cyclotomic polynomials. Which powers of cyclotomic polynomials occur? The ai ...

Springer Int Publ Ag2024

The multivariate Serre conjecture ring

Luc Guyot

It is well-known that for any integral domain R, the Serre conjecture ring R(X), i.e., the localization of the univariate polynomial ring R[X] at monic polynomials, is a Bezout domain of Krull dimension

Academic Press Inc Elsevier Science2023

Metastability of the Potts Ferromagnet on Random Regular Graphs

Jean Bernoulli Ravelomanana

We study the performance of Markov chains for the q-state ferromagnetic Potts model on random regular graphs. While the cases of the grid and the complete graph are by now well-understood, the case of random regular graphs has resisted a detailed analysis ...

SPRINGER2023

Distributional Regression and Autoregression via Optimal Transport

Laya Ghodrati

We present a framework for performing regression when both covariate and response are probability distributions on a compact and convex subset of

\R^d

. Our regression model is based on the theory of optimal transport and links the conditional Fr'echet m ...

EPFL2023

Hidden Markov Modeling Over Graphs

Ali H. Sayed, Stefan Vlaski, Virginia Bordignon, Mert Kayaalp

This work proposes a multi-agent filtering algorithm over graphs for finite-state hidden Markov models (HMMs), which can be used for sequential state estimation or for tracking opinion formation over dynamic social networks. We show that the difference fro ...

IEEE2022

A note on universal inference

Anthony Christopher Davison, Timmy Rong Tian Tse

Universal inference enables the construction of confidence intervals and tests without regularity conditions by splitting the data into two parts and appealing to Markov's inequality. Previous investigations have shown that the cost of this generality is a ...

WILEY2022

Finite free convolutions of polynomials

Adam Wade Marcus

We study three convolutions of polynomials in the context of free probability theory. We prove that these convolutions can be written as the expected characteristic polynomials of sums and products of unitarily invariant random matrices. The symmetric addi ...

SPRINGER HEIDELBERG2022

A PCP Theorem for Interactive Proofs and Applications

Alessandro Chiesa

The celebrated PCP Theorem states that any language in NP can be decided via a verifier that reads O(1) bits from a polynomially long proof. Interactive oracle proofs (IOP), a generalization of PCPs, allow the verifier to interact with the prover for multi ...

SPRINGER INTERNATIONAL PUBLISHING AG2022

Fast deterministic and randomized algorithms for low-rank approximation, matrix functions, and trace estimation

Alice Cortinovis

In this thesis we propose and analyze algorithms for some numerical linear algebra tasks: finding low-rank approximations of matrices, computing matrix functions, and estimating the trace of matrices. In the first part, we consider algorithms for building ...

EPFL2022

The spectral bias of polynomial neural networks

Volkan Cevher, Moulik Choraria, Leello Tadesse Dadi, Grigorios Chrysos

Polynomial neural networks (PNNs) have been recently shown to be particularly effective at image generation and face recognition, where high-frequency information is critical. Previous studies have revealed that neural networks demonstrate a spectral bias ...

2022

Distributionally Robust Optimization with Markovian Data

Daniel Kuhn, Tobias Sutter, Mengmeng Li

We study a stochastic program where the probability distribution of the uncertain problem parameters is unknown and only indirectly observed via finitely many correlated samples generated by an unknown Markov chain with d states. We propose a data-driven d ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2021

Fast Bayesian estimation of spatial count data models

Prateek Bansal, Rico Krüger

Spatial count data models are used to explain and predict the frequency of phenomena such as traffic accidents in geographically distinct entities such as census tracts or road segments. These models are typically estimated using Bayesian Markov chain Mont ...

2021

A (2+epsilon)-Approximation Algorithm for Preemptive Weighted Flow Time on a Single Machine

Lars Rohwedder

Weighted flow time is a fundamental and very well-studied objective function in scheduling. In this paper, we study the setting of a single machine with preemptions. ...

ASSOC COMPUTING MACHINERY2021

Unbiased Monte Carlo cluster updates with autoregressive neural networks

Giuseppe Carleo, Dian Wu, Riccardo Rossi

Efficient sampling of complex high-dimensional probability distributions is a central task in computational science. Machine learning methods like autoregressive neural networks, used with Markov chain Monte Carlo sampling, provide good approximations to s ...

AMER PHYSICAL SOC2021

Distributed Learning in Non-Convex Environments-Part I: Agreement at a Linear Rate

Ali H. Sayed, Stefan Vlaski

Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments. Most available wor ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Markov cubature rules for polynomial processes

Damir Filipovic, Martin Larsson, Sergio Andres Pulido Nino

We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rul ...

ELSEVIER2020

Polynomial Evaluation on Superscalar Architecture, Applied to the Elementary Function e(x)

Felix Schürmann, Timothée Ewart, Fabien Jonathan Delalondre, Francesco Cremonesi

The evaluation of small degree polynomials is critical for the computation of elementary functions. It has been extensively studied and is well documented. In this article, we evaluate existing methods for polynomial evaluation on superscalar architecture. ...

2020

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

,

b \in \Z^m

,

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

Interpolatory Rational Model Order Reduction of Parametric Problems Lacking Uniform Inf-Sup Stability

Davide Pradovera

We present a technique for the approximation of a class of Hilbert space--valued maps which arise within the framework of model order reduction (MOR) for parametric partial differential equations, whose solution map has a meromorphic structure. Our MOR str ...

2020