Related papers: sparta: Sparse Tables and their Algebra with a Vie…
We propose a method for recovering the structure of a sparse undirected graphical model when very few samples are available. The method decides about the presence or absence of bonds between pairs of variable by considering one pair at a…
As illustrated by the success of integer linear programming, linear integer arithmetic is a powerful tool for modelling combinatorial problems. Furthermore, the probabilistic extension of linear programming has been used to formulate…
We develop a new randomized iterative algorithm---stochastic dual ascent (SDA)---for finding the projection of a given vector onto the solution space of a linear system. The method is dual in nature: with the dual being a non-strongly…
Statistical sufficiency formalizes the notion of data reduction. In the decision theoretic interpretation, once a model is chosen all inferences should be based on a sufficient statistic. However, suppose we start with a set of procedures…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
We consider the problem of recovering conditional independence relationships between $p$ jointly distributed Hilbertian random elements given $n$ realizations thereof. We operate in the sparse high-dimensional regime, where $n \ll p$ and no…
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…
Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…
Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as…
We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for mathematical theory as well as performance for finite-sample data. We present a…
Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…
In this article the package High-dimensional Metrics (\texttt{hdm}) is introduced. It is a collection of statistical methods for estimation and quantification of uncertainty in high-dimensional approximately sparse models. It focuses on…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
Curse of Dimensionality is an unavoidable challenge in statistical probability models, yet diffusion models seem to overcome this limitation, achieving impressive results in high-dimensional data generation. Diffusion models assume that…
Feature-distributed data, referred to data partitioned by features and stored across multiple computing nodes, are increasingly common in applications with a large number of features. This paper proposes a two-stage relaxed greedy algorithm…
Complex analyses involving multiple, dependent random quantities often lead to graphical models - a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes. To develop statistical…
In high-dimensional settings, Canonical Correlation Analysis (CCA) often fails, and existing sparse methods force an untenable choice between computational speed and statistical rigor. This work introduces a fast and provably consistent…
Probabilistic programs encode stochastic models as ordinary-looking programs with primitives for sampling numbers from predefined distributions and conditioning. Their applications include, among many others, machine learning and modeling…
Sparse Triangular Solve (SpTRSV) is an important computational kernel used in the solution of sparse linear algebra systems in many scientific and engineering applications. It is diffcult to parallelize SpTRSV in today's architectures. The…