This paper introduces the R package spca, which provides a computational framework for least squares sparse principal component analysis (LS-SPCA). Unlike other SPCA methods, LS-SPCA generates uncorrelated sparse principal components (sPCs) that effectively maximize the explained variance while maintaining strong correlations with standard principal components (PCs). The framework also includes more computationally efficient variants that produce mildly correlated sPCs, which often have lower cardinality while explaining equal or greater variance than the LS-SPCA optimal sPCs. The spca package is built on an efficient C++ backend for matrix computations, with distinct engines for tall and fat matrices, and a flexible R frontend. The user interface offers several options for computing sPCs, such as deciding whether sparsification should stop when a threshold for cumulative variance explained or R2 with the PCs is reached, and choosing between simple forward selection, stepwise forward selection, or backward elimination for variable selection. In addition to the print(), summary(), and plot() methods, the package includes tools for comparing different "spca" solutions, grouping sparse loadings, and representing foreign SPCA solutions as "spca" objects. This article demonstrates with real datasets the use of the package in a typical LS-SPCA workflow and briefly contrasts LS-SPCA with conventional SPCA solutions . Then it compares different LS-SPCA solutions obtained from the dataset. Finally, the performance of spca on large tall and fat matrices is discussed, showing that spca offers a computationally efficient alternative for computing interpretable sPCs.

Recent years have revealed an unprecedented demand for AI-based technology, leading to a common setting where immense data is distributed across multiple locations. This creates a communication bottleneck among the storage facilities, often aiming to jointly solve tasks of small solution size k from input of astronomically large size n. Motivated by federated and distributed machine learning applications, we study two fundamental optimization problems, maximum weight matroid independent set (MW-IS) and maximum weight matching (MWM), in a zero communication computational model. In this model, the data is dispersed between m servers. Without any communication, each server has to send a message to a central coordinator which is required to compute an optimal solution for the original (large) instance.

Neural posterior estimation has emerged as a powerful tool for amortized inference, with growing adoption across scientific and applied domains. In many of these applications, the conditioning variable is a set of observations whose elements depend not only on the target but also on unknown factors shared across the set. Optimal inference therefore requires treating the set jointly, which in turn requires training the estimator at the deployment set size -- a regime where memory and compute quickly become prohibitive. We introduce a simple, theoretically grounded strategy that decouples representation learning from posterior modeling. Our method trains a mean-pool Deep Set on sets of size at most two, producing an encoder that generalizes to arbitrary set sizes. The inference head is then finetuned on pre-aggregated embeddings, making training cost essentially independent of the deployment set size N. Across scalar, image, multi-view 3D, molecular, and high-dimensional conditional generation benchmarks with N in the thousands, our approach matches or outperforms standard baselines at a fraction of the compute.

Combination therapy refers to the use of multiple treatments - such as surgery, medication, and behavioral therapy - to cure a single disease, and has become a cornerstone for treating various conditions including cancer, HIV, and depression. All possible combinations of treatments lead to a collection of treatment regimens (i.e., policies) with mixed scopes, or what physicians could observe and which actions they should take depending on the context. In this paper, we investigate the online reinforcement learning setting for optimizing the policy space with mixed scopes. In particular, we develop novel online algorithms that achieve sublinear regret compared to an optimal agent deployed in the environment. The regret bound has a dependency on the maximal cardinality of the induced state-action space associated with mixed scopes. We further introduce a canonical representation for an arbitrary subset of interventional distributions given a causal diagram, which leads to a non-trivial, minimal representation of the model parameters.

In this paper we present a practical solution with performance guarantees to the problem of dimensionality reduction for very large scale sparse matrices. We show applications of our approach to computing the Principle Component Analysis (PCA) of any n dmatrix, using one pass over the stream of its rows. Our solution uses coresets: a scaled subset of the n rows that approximates their sum of squared distances to every k-dimensional affine subspace. An open theoretical problem has been to compute such a coreset that is independent of both n and d. An open practical problem has been to compute a non-trivial approximation to the PCA of very large but sparse databases such as the Wikipedia document-term matrix in a reasonable time. We answer both of these questions affirmatively. Our main technical result is a new framework for deterministic coreset constructions based on a reduction to the problem of counting items in a stream.

Neural Information Processing Systems http://nips.cc/

We study causal subset selection with Directed Information as the measure of prediction causality. Two typical tasks, causal sensor placement and covariate selection, are correspondingly formulated into cardinality constrained directed information maximizations. To attack the NP-hard problems, we show that the first problem is submodular while not necessarily monotonic. And the second one is "nearly" submodular. To substantiate the idea of approximate submodularity, we introduce a novel quantity, namely submodularity index (SmI), for general set functions. Moreover, we show that based on SmI, greedy algorithm has performance guarantee for the maximization of possibly non-monotonic and non-submodular functions, justifying its usage for a much broader class of problems. We evaluate the theoretical results with several case studies, and also illustrate the application of the subset selection to causal structure learning.