Related papers: Randomized Complexity of Vector-Valued Approximati…
Random effect models are popular statistical models for detecting and correcting spurious sample correlations due to hidden confounders in genome-wide gene expression data. In applications where some confounding factors are known,…
The node-averaged complexity of a distributed algorithm running on a graph $G=(V,E)$ is the average over the times at which the nodes $V$ of $G$ finish their computation and commit to their outputs. We study the node-averaged complexity for…
We consider the problem of estimating the arithmetic average of a finite collection of real vectors stored in a distributed fashion across several compute nodes subject to a communication budget constraint. Our analysis does not rely on any…
We consider the problem of learning a coefficient vector $x_{0}$ in $R^{N}$ from noisy linear observations $y=Fx_{0}+w$ in $R^{M}$ in the high dimensional limit $M,N$ to infinity with $\alpha=M/N$ fixed. We provide a rigorous derivation of…
We study the approximability of the NP-complete \textsc{Maximum Minimal Feedback Vertex Set} problem. Informally, this natural problem seems to lie in an intermediate space between two more well-studied problems of this type:…
We introduce a general framework for the reconstruction of vector-valued functions from finite and possibly noisy data, acquired through a known measurement operator. The reconstruction is done by the minimization of a loss functional…
The generalization gap of a classifier is related to the complexity of the set of functions among which the classifier is chosen. We study a family of low-complexity classifiers consisting of thresholding a random one-dimensional feature.…
This paper addresses the general problem of domain adaptation which arises in a variety of applications where the distribution of the labeled sample available somewhat differs from that of the test data. Building on previous work by…
Shuffled regression and unlinked regression represent intriguing challenges that have garnered considerable attention in many fields, including but not limited to ecological regression, multi-target tracking problems, image denoising, etc.…
In statistical setting of the pattern recognition problem the number of examples required to approximate an unknown labelling function is linear in the VC dimension of the target learning class. In this work we consider the question whether…
Missing values arise in most real-world data sets due to the aggregation of multiple sources and intrinsically missing information (sensor failure, unanswered questions in surveys...). In fact, the very nature of missing values usually…
Matrix completion is a well-studied problem with many machine learning applications. In practice, the problem is often solved by non-convex optimization algorithms. However, the current theoretical analysis for non-convex algorithms relies…
There has been substantial interest in estimating the value of a graph parameter, i.e., of a real-valued function defined on the set of finite graphs, by querying a randomly sampled substructure whose size is independent of the size of the…
In the stochastic matching problem, we are given a general (not necessarily bipartite) graph $G(V,E)$, where each edge in $E$ is realized with some constant probability $p > 0$ and the goal is to compute a bounded-degree (bounded by a…
We consider minimizing an objective function subject to constraints defined by the intersection of lower-level sets of convex functions. We study two cases: (i) strongly convex and Lipschitz-smooth objective function and (ii) convex but…
We propose a framework for sensitivity analysis of linear programs (LPs) in minimization form, allowing for simultaneous perturbations in the objective coefficients and right-hand sides, where the perturbations are modeled in a compact,…
In this thesis we study adaptive nonparametric regression with noise misspecification and the complexity of approximation of random fields in dependence of the dimension. First, we consider the problem of pointwise estimation in…
In this paper, we investigate the problem of classifying feature vectors with mutually independent but non-identically distributed elements. First, we show the importance of this problem. Next, we propose a classifier and derive an…
Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…
Adaptivity is an important feature of data analysis---the choice of questions to ask about a dataset often depends on previous interactions with the same dataset. However, statistical validity is typically studied in a nonadaptive model,…