Related papers: Statistical Query Algorithms and Low-Degree Tests …

Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…

In the supervised learning domain, considering the recent prevalence of algorithms with high computational cost, the attention is steering towards simpler, lighter, and less computationally extensive training and inference approaches. In…

Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…

Single-Index Models are high-dimensional regression problems with planted structure, whereby labels depend on an unknown one-dimensional projection of the input via a generic, non-linear, and potentially non-deterministic transformation. As…

The sparsity constrained rank-one matrix approximation problem is a difficult mathematical optimization problem which arises in a wide array of useful applications in engineering, machine learning and statistics, and the design of…

Motivated by multi-task and meta-learning approaches, we consider the problem of learning structure shared by tasks or users, such as shared low-rank representations or clustered structures. While all previous works focus on well-specified…

We introduce statistical constraints, a declarative modelling tool that links statistics and constraint programming. We discuss two statistical constraints and some associated filtering algorithms. Finally, we illustrate applications to…

Singular value decomposition (SVD) based principal component analysis (PCA) breaks down in the high-dimensional and limited sample size regime below a certain critical eigen-SNR that depends on the dimensionality of the system and the…

A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…

Model selection consistency in the high-dimensional regression setting can be achieved only if strong assumptions are fulfilled. We therefore suggest to pursue a different goal, which we call a minimal class of models. The minimal class of…

The least-squares support vector machine is a frequently used kernel method for non-linear regression and classification tasks. Here we discuss several approximation algorithms for the least-squares support vector machine classifier. The…

The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In…

Automating algorithm configuration is growing increasingly necessary as algorithms come with more and more tunable parameters. It is common to tune parameters using machine learning, optimizing performance metrics such as runtime and…

We introduce an extension to the CLRS algorithmic learning benchmark, prioritizing scalability and the utilization of sparse representations. Many algorithms in CLRS require global memory or information exchange, mirrored in its execution…

Statistical query (SQ) algorithms are algorithms that have access to an {\em SQ oracle} for the input distribution $D$ instead of i.i.d.~ samples from $D$. Given a query function $\phi:X \rightarrow [-1,1]$, the oracle returns an estimate…

Consider the setting where a $\rho$-sparse Rademacher vector is planted in a random $d$-dimensional subspace of $R^n$. A classical question is how to recover this planted vector given a random basis in this subspace. A recent result by…

Quantiles are very important statistics information used to describe the distribution of datasets. Given the quantiles of a dataset, we can easily know the distribution of the dataset, which is a fundamental problem in data analysis.…

A conditional sampling oracle for a probability distribution D returns samples from the conditional distribution of D restricted to a specified subset of the domain. A recent line of work (Chakraborty et al. 2013 and Cannone et al. 2014)…

The theoretical information threshold for the planted clique problem is $2\log_2(N)$, however no polynomial algorithm is known to recover a planted clique of size $O(N^{1/2-\epsilon})$, $\epsilon>0$. In this paper we will apply a standard…

High-dimensional tensor-valued predictors arise in modern applications, increasingly as learned representations from neural networks. Existing tensor classification methods rely on sparsity or Tucker structures and often lack theoretical…