Related papers: Nonparametric statistical inference for the contex…
Suppose one has a collection of parameters indexed by a (possibly infinite dimensional) set. Given data generated from some distribution, the objective is to estimate the maximal parameter in this collection evaluated at this distribution.…
In this paper, we study the problem of finding a minimum weight spanning tree that contains each vertex in a given subset $V_{\rm NT}$ of vertices as an internal vertex. This problem, called Minimum Weight Non-Terminal Spanning Tree,…
This paper introduces a novel nonparametric method for estimating high-dimensional dynamic covariance matrices with multiple conditioning covariates, leveraging random forests and supported by robust theoretical guarantees. Unlike…
Language models (LMs) are trained on billions of tokens in an attempt to recover the true language distribution. Still, vanilla random sampling from LMs yields low quality generations. Decoding algorithms attempt to restrict the LM…
We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…
In some memory-constrained settings like IoT devices and over-the-network data pipelines, it can be advantageous to have smaller contextual embeddings. We investigate the efficacy of projecting contextual embedding data (BERT) onto a…
This paper provides new uniform rate results for kernel estimators of absolutely regular stationary processes that are uniform in the bandwidth and in infinite-dimensional classes of dependent variables and regressors. Our results are…
We consider stochastic processes with (or without) memory whose evolution is encoded by a finite or infinite rooted tree. The main goal is to compare the entropy rates of a given base process and a second one, to be considered as a…
The goal of this paper is to provide some tools for nonparametric estimation and inference in psychological and economic experiments. We consider an experimental framework in which each of $n$subjects provides $T$ responses to a vector of…
Embedding data into vector spaces is a very popular strategy of pattern recognition methods. When distances between embeddings are quantized, performance metrics become ambiguous. In this paper, we present an analysis of the ambiguity…
We study the problem of grammar-constrained context-free language reachability in graphs, focusing on complexity and empirical performance. We present an algorithmic framework for evaluating reachability queries constrained by context-free…
In a multivariate nonparametric regression setting we construct explicit asymptotic uniform confidence bands for centered purely random forests. Since the most popular example in this class of random forests, namely the uniformly centered…
Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. For a wide class of intrinsically ergodic subshifts over a finite alphabet, we show that the space of…
This paper is part of the general project of proof mining, developed by Kohlenbach. By "proof mining" we mean the logical analysis of mathematical proofs with the aim of extracting new numerically relevant information hidden in the proofs.…
We suggest a new approach to hypothesis testing for ergodic and stationary processes. In contrast to standard methods, the suggested approach gives a possibility to make tests, based on any lossless data compression method even if the…
Parameter estimation in a class of heteroscedastic time series models is investigated. The existence of conditional least-squares and conditional likelihood estimators is proved. Their consistency and their asymptotic normality are…
Spectral estimation is a fundamental problem for time series analysis, which is widely applied in economics, speech analysis, seismology, and control systems. The asymptotic convergence theory for classical, non-parametric estimators, is…
Traditional parametric econometric models often rely on rigid functional forms, while nonparametric techniques, despite their flexibility, frequently lack interpretability. This paper proposes a parsimonious alternative by modeling the…
In retrieval applications, binary hashes are known to offer significant improvements in terms of both memory and speed. We investigate the compression of sentence embeddings using a neural encoder-decoder architecture, which is trained by…
Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiply-recursive complexity lower bounds. We refine…