Related papers: Estimating the inverse trace using random forests …

We consider a multivariate distributional recursion of sum-type as arising in the probabilistic analysis of algorithms and random trees. We prove an upper tail bound for the solution using Chernoff's bounding technique by estimating the…

In this paper, we study the trace regression when a matrix of parameters B* is estimated via the convex relaxation of a rank-regularized regression or via regularized non-convex optimization. It is known that these estimators satisfy…

This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models,…

We revisit the derivation of the density of states of sparse random matrices. We derive a recursion relation that allows one to compute the spectrum of the matrix of incidence for finite trees that determines completely the low…

Inverse reinforcement learning aims to infer the reward function that explains expert behavior observed through trajectories of state--action pairs. A long-standing difficulty in classical IRL is the non-uniqueness of the recovered reward:…

In high-dimensional linear models, sparsity is often exploited to reduce variability and achieve parsimony. Equi-sparsity, where one assumes that predictors can be aggregated into groups sharing the same effects, is an alternative…

We study ridge estimation of the precision matrix in the high-dimensional setting where the number of variables is large relative to the sample size. We first review two archetypal ridge estimators and note that their utilized penalties do…

The transmission of a vertex in a connected graph is the sum of distances from that vertex to all the other vertices. A connected graph is transmission irregular if any two distinct vertices have different transmissions. We present an…

Partial differential equations are central to describing many physical phenomena. In many applications these phenomena are observed through a sensor network, with the aim of inferring their underlying properties. Leveraging from certain…

We provide estimators for a large class of inverse problems, including nonlinear inverse problems. Using complexity regularization technics we provide adaptive estimators achieving the best rate over the collection of models.

The loss and the norm of its gradient separate the healthy and the pathological regimes of neural-network training only weakly, whilst the curvature of the empirical risk differs qualitatively between them but is inaccessible explicitly at…

We introduce a general approach to traces that we consider as linear continuous functionals on some function space where we focus on some special choices for that space. This leads to an integral calculus for the computation of the precise…

Trajectory Reconstruction (TR) is vital for accurately mapping movement patterns and validating analyses, especially in fields like robotics, biomechanics, and environmental tracking, where data might be missing or affected by outliers.…

Normalizing flows attempt to model an arbitrary probability distribution through a set of invertible mappings. These transformations are required to achieve a tractable Jacobian determinant that can be used in high-dimensional scenarios.…

Randomising networks using a naive `accept-all' edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities for…

Big Data is one of the major challenges of statistical science and has numerous consequences from algorithmic and theoretical viewpoints. Big Data always involve massive data but they also often include online data and data heterogeneity.…

Regression trees are a popular machine learning algorithm that fit piecewise constant models by recursively partitioning the predictor space. This paper focuses on statistical inference for a data-dependent model obtained from a fitted…

We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactification; it also gives a representation of the limit in…

Tree ensembles such as random forests and boosted trees are accurate but difficult to understand, debug and deploy. In this work, we provide the inTrees (interpretable trees) framework that extracts, measures, prunes and selects rules from…

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…