Related papers: COMBSS: Best Subset Selection via Continuous Optim…
The problem of column subset selection asks for a subset of columns from an input matrix such that the matrix can be reconstructed as accurately as possible within the span of the selected columns. A natural extension is to consider a…
Least squares (LS)-based subset selection methods are popular in linear regression modeling. Best subset selection (BS) is known to be NP-hard and has a computational cost that grows exponentially with the number of predictors. Recently,…
This paper deals with the problem of finding the globally optimal subset of h elements from a larger set of n elements in d space dimensions so as to minimize a quadratic criterion, with an special emphasis on applications to computing the…
Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…
We explore algorithms and limitations for sparse optimization problems such as sparse linear regression and robust linear regression. The goal of the sparse linear regression problem is to identify a small number of key features, while the…
We consider the problem of best subset selection (BSS) under high-dimensional sparse linear regression model. Recently, Guo et al. (2020) showed that the model selection performance of BSS depends on a certain identifiability margin, a…
Sub-sampling is a common and often effective method to deal with the computational challenges of large datasets. However, for most statistical models, there is no well-motivated approach for drawing a non-uniform subsample. We show that the…
Consider a collection of competing machine learning algorithms. Given their performance on a benchmark of datasets, we would like to identify the best performing algorithm. Specifically, which algorithm is most likely to rank highest on a…
Neural networks and deep learning are changing the way that artificial intelligence is being done. Efficiently choosing a suitable network architecture and fine-tune its hyper-parameters for a specific dataset is a time-consuming task given…
Compressed sensing (CS) has emerged to overcome the inefficiency of Nyquist sampling. However, traditional optimization-based reconstruction is slow and can not yield an exact image in practice. Deep learning-based reconstruction has been a…
Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Combinatorial optimisation is the practice of selecting the best constituent…
In exciting new work, Bertsimas et al. (2016) showed that the classical best subset selection problem in regression modeling can be formulated as a mixed integer optimization (MIO) problem. Using recent advances in MIO algorithms, they…
Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted…
Incorporating feature selection into a classification or regression method often carries a number of advantages. In this paper we formalize feature selection specifically from a discriminative perspective of improving…
Data subset selection from a large number of training instances has been a successful approach toward efficient and cost-effective machine learning. However, models trained on a smaller subset may show poor generalization ability. In this…
Bayesian coresets have emerged as a promising approach for implementing scalable Bayesian inference. The Bayesian coreset problem involves selecting a (weighted) subset of the data samples, such that the posterior inference using the…
Linear mixed models (LMMs), which incorporate fixed and random effects, are key tools for analyzing heterogeneous data, such as in personalized medicine. Nowadays, this type of data is increasingly wide, sometimes containing thousands of…
A coreset is a subset of the training set, using which a machine learning algorithm obtains performances similar to what it would deliver if trained over the whole original data. Coreset discovery is an active and open line of research as…
Large-scale supervised classification algorithms, especially those based on deep convolutional neural networks (DCNNs), require vast amounts of training data to achieve state-of-the-art performance. Decreasing this data requirement would…
The sparse regression problem, also known as best subset selection problem, can be cast as follows: Given a set $S$ of $n$ points in $\mathbb{R}^d$, a point $y\in \mathbb{R}^d$, and an integer $2 \leq k \leq d$, find an affine combination…