Related papers: On matrix balancing and eigenvector computation
Bayesian optimization is a popular framework for efficiently tackling black-box search problems. As a rule, these algorithms operate by iteratively choosing what to evaluate next until some predefined budget has been exhausted. We…
Modern instance-based model-agnostic explanation methods (LIME, SHAP, L2X) are of great use in data-heavy industries for model diagnostics, and for end-user explanations. These methods generally return either a weighting or subset of input…
We introduce a new randomization procedure for experiments based on the cube method, which achieves near-exact covariate balance. This ensures compliance with standard balance tests and allows for balancing on many covariates, enabling more…
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete…
Robots should be able to learn complex behaviors from human demonstrations. In practice, these human-provided datasets are inevitably imbalanced: i.e., the human demonstrates some subtasks more frequently than others. State-of-the-art…
The randomized Kaczmarz method is an iterative algorithm that solves overdetermined systems of linear equations. Recently, the method was extended to systems of equalities and inequalities by Leventhal and Lewis. Even more recently, Needell…
Matrix completion is the problem of recovering a low rank matrix by observing a small fraction of its entries. A series of recent works [KOM12,JNS13,HW14] have proposed fast non-convex optimization based iterative algorithms to solve this…
Eigenvalue estimates that are optimal in some sense have self-evident appeal and leave estimators with a sense of virtue and economy. So, it is natural that ongoing searches for effective strategies for difficult tasks such as estimating…
Random matrices tend to be well conditioned, and we employ this well known property to advance matrix computations. We prove that our algorithms employing Gaussian random matrices are efficient, but in our tests the algorithms have…
A machine learning model is calibrated if its predicted probability for an outcome matches the observed frequency for that outcome conditional on the model prediction. This property has become increasingly important as the impact of machine…
This paper aims to address two fundamental challenges arising in eigenvector estimation and inference for a low-rank matrix from noisy observations: (1) how to estimate an unknown eigenvector when the eigen-gap (i.e. the spacing between the…
Gaussian processes provide probabilistic surrogates for various applications including classification, uncertainty quantification, and optimization. Using a gradient-enhanced covariance matrix can be beneficial since it provides a more…
Neural Networks can perform poorly when the training label distribution is heavily imbalanced, as well as when the testing data differs from the training distribution. In order to deal with shift in the testing label distribution, which…
We consider eigenvalue condition numbers and backward errors for a class of symmetric nonlinear eigenvalue problems with eigenvector nonlinearities. For both of these quantities, we derive explicit and computable expressions that can be…
There are many real-world classification problems wherein the issue of data imbalance (the case when a data set contains substantially more samples for one/many classes than the rest) is unavoidable. While under-sampling the problematic…
The design of high-precision sensing devises becomes ever more difficult and expensive. At the same time, the need for precise calibration of these devices (ranging from tiny sensors to space telescopes) manifests itself as a major…
In the context of Visual Question Answering (VQA) and Agentic AI, calibration refers to how closely an AI system's confidence in its answers reflects their actual correctness. This aspect becomes especially important when such systems…
This paper deals with a new middle path approach developed for reducing alignment calculations in BLAST algorithm. This is a new step which is introduced in BLAST algorithm in between the ungapped and gapped alignments. This step of middle…
This paper introduces a computationally efficient method that converges globally to B-stationary points of mathematical programs with equilibrium constraints (MPECs). B-stationarity is necessary for optimality and means that no feasible…
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…