Related papers: Poisson Regression in one Covariate on Massive Dat…
We consider the problem of selecting a small subset of representative variables from a large dataset. In the computer science literature, this dimensionality reduction problem is typically formalized as Column Subset Selection (CSS).…
Datasets with sheer volume have been generated from fields including computer vision, medical imageology, and astronomy whose large-scale and high-dimensional properties hamper the implementation of classical statistical models. To tackle…
One-shot decision making is required in situations in which we can evaluate a fixed number of solution candidates but do not have any possibility for further, adaptive sampling. Such settings are frequently encountered in neural network…
Modern statistical analysis often encounters datasets with large sizes. For these datasets, conventional estimation methods can hardly be used immediately because practitioners often suffer from limited computational resources. In most…
Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…
The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…
Labelling data is a major practical bottleneck in training and testing classifiers. Given a collection of unlabelled data points, we address how to select which subset to label to best estimate test metrics such as accuracy, $F_1$ score or…
Subsampling is a general statistical method developed in the 1990s aimed at estimating the sampling distribution of a statistic $\hat \theta _n$ in order to conduct nonparametric inference such as the construction of confidence intervals…
In semi-supervised learning, the prevailing understanding suggests that observing additional unlabeled samples improves estimation accuracy for linear parameters only in the case of model misspecification. In this work, we challenge such a…
A major challenge for building statistical models in the big data era is that the available data volume far exceeds the computational capability. A common approach for solving this problem is to employ a subsampled dataset that can be…
Extraordinary amounts of data are being produced in many branches of science. Proven statistical methods are no longer applicable with extraordinary large data sets due to computational limitations. A critical step in big data analysis is…
Given a sample of size $N$, it is often useful to select a subsample of smaller size $n<N$ to be used for statistical estimation or learning. Such a data selection step is useful to reduce the requirements of data labeling and the…
Given $m$ $d$-dimensional responsors and $n$ $d$-dimensional predictors, sparse regression finds at most $k$ predictors for each responsor for linear approximation, $1\leq k \leq d-1$. The key problem in sparse regression is subset…
If the assumed model does not accurately capture the underlying structure of the data, a statistical method is likely to yield sub-optimal results, and so model selection is crucial in order to conduct any statistical analysis. However, in…
Large-scale statistical analysis of data sets associated with genome sequences plays an important role in modern biology. A key component of such statistical analyses is the computation of $p$-values and confidence bounds for statistics…
Factor analysis for high-dimensional data is a canonical problem in statistics and has a wide range of applications. However, there is currently no factor model tailored to effectively analyze high-dimensional count responses with…
We develop and analyze data subsampling techniques for Poisson regression, the standard model for count data $y\in\mathbb{N}$. In particular, we consider the Poisson generalized linear model with ID- and square root-link functions. We…
The problem of best subset selection in linear regression is considered with the aim to find a fixed size subset of features that best fits the response. This is particularly challenging when the total available number of features is very…
We study the optimal sample complexity of variable selection in linear regression under general design covariance, and show that subset selection is optimal while under standard complexity assumptions, efficient algorithms for this problem…
The use of massive survival data has become common in survival analysis. In this study, a subsampling algorithm is proposed for the Cox proportional hazards model with time-dependent covariates when the sample is extraordinarily large but…