Algorithmic stability is a concept from learning theory that expresses the degree to which changes to the input data (e. g., removal of a single data point) may affect the outputs of a regression algorithm.
In a binary classification problem where the goal is to fit an accurate predictor, the presence of corrupted labels in the training data set may create an additional challenge.
An important factor to guarantee a fair use of data-driven recommendation systems is that we should be able to communicate their uncertainty to decision makers.
We consider the problem of distribution-free predictive inference, with the goal of producing predictive coverage guarantees that hold conditionally rather than marginally.
Statistics Theory Statistics Theory
Two common approaches in low-rank optimization problems are either working directly with a rank constraint on the matrix variable, or optimizing over a low-rank factorization so that the rank constraint is implicitly ensured.
Optimization and Control
Like the conditional randomization test of Cand\`es et al. (2018), our test relies on the availability of an approximation to the distribution of $X \mid Z$.
Methodology Statistics Theory Statistics Theory
Instead, a general class of thresholding operators, lying between hard thresholding and soft thresholding, is shown to be optimal with the strongest possible convergence guarantee among all thresholding operators.
We analyze the performance of alternating minimization for loss functions optimized over two variables, where each variable may be restricted to lie in some potentially nonconvex constraint set.
There is a significant literature on methods for incorporating knowledge into multiple testing procedures so as to improve their power and precision.
We propose the group knockoff filter, a method for false discovery rate control in a linear regression setting where the features are grouped, and we would like to select a set of relevant groups which have a nonzero effect on the response.
In many practical applications of multiple hypothesis testing using the False Discovery Rate (FDR), the given hypotheses can be naturally partitioned into groups, and one may not only want to control the number of false discoveries (wrongly rejected null hypotheses), but also the number of falsely discovered groups of hypotheses (we say a group is falsely discovered if at least one hypothesis within that group is rejected, when in reality the group contains only nulls).
The robust principal component analysis (RPCA) problem seeks to separate low-rank trends from sparse outlierswithin a data matrix, that is, to approximate a $n\times d$ matrix $D$ as the sum of a low-rank matrix $L$ and a sparse matrix $S$. We examine the robust principal component analysis (RPCA) problem under data compression, wherethe data $Y$ is approximately given by $(L + S)\cdot C$, that is, a low-rank $+$ sparse data matrix that has been compressed to size $n\times m$ (with $m$ substantially smaller than the original dimension $d$) via multiplication witha compression matrix $C$.
Undirected graphical models are used extensively in the biological and social sciences to encode a pattern of conditional independences between variables, where the absence of an edge between two nodes $a$ and $b$ indicates that the corresponding two variables $X_a$ and $X_b$ are believed to be conditionally independent, after controlling for all other measured variables.