Related papers: Subspace Estimation from Incomplete Observations: …

Problem statement: Clustering has a number of techniques that have been developed in statistics, pattern recognition, data mining, and other fields. Subspace clustering enumerates clusters of objects in all subspaces of a dataset. It tends…

Timely detection of abrupt anomalies is crucial for real-time monitoring and security of modern systems producing high-dimensional data. With this goal, we propose effective and scalable algorithms. Proposed algorithms are nonparametric as…

This paper is concerned with high-dimensional panel data models where the number of regressors can be much larger than the sample size. Under the assumption that the true parameter vector is sparse we propose a panel-Lasso estimator and…

We show how random subspace methods can be adapted to estimating local projections with many controls. Random subspace methods have their roots in the machine learning literature and are implemented by averaging over regressions estimated…

Iterative steady-state solvers are widely used in computational fluid dynamics. Unfortunately, it is difficult to obtain steady-state solution for unstable problem caused by physical instability and numerical instability. Optimization is a…

Given two distributions $\mathcal{P}$ and $\mathcal{Q}$ over a high-dimensional domain $\{0,1\}^n$, and a parameter $\varepsilon$, the goal of distance estimation is to determine the statistical distance between $\mathcal{P}$ and…

We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…

Space complexity is a critical factor in various computational models, including streaming, parallel/distributed computing, and communication complexity. We study the space complexity of the minimum-cost flow problem, a generalization of…

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or…

AI inference scaling is often tuned through 1D heuristics (a fixed reasoning pass) or 2D bivariate trade-offs (e.g., accuracy vs. compute), which fail to consider cost and latency constraints. We introduce a 3D optimization framework that…

Earth Observation imagery can capture rare and unusual events, such as disasters and major landscape changes, whose visual appearance contrasts with the usual observations. Deep models trained on common remote sensing data will output…

The distinct elements problem is one of the fundamental problems in streaming algorithms --- given a stream of integers in the range $\{1,\ldots,n\}$, we wish to provide a $(1+\varepsilon)$ approximation to the number of distinct elements…

Neural Jump ODEs model the conditional expectation between observations by neural ODEs and jump at arrival of new observations. They have demonstrated effectiveness for fully data-driven online forecasting in settings with irregular and…

Score-based generative models, which transform noise into data by learning to reverse a diffusion process, have become a cornerstone of modern generative AI. This paper contributes to establishing theoretical guarantees for the probability…

Stochastic optimization naturally arises in machine learning. Efficient algorithms with provable guarantees, however, are still largely missing, when the objective function is nonconvex and the data points are dependent. This paper studies…

We study sublinear algorithms for two fundamental graph problems, MAXCUT and correlation clustering. Our focus is on constructing core-sets as well as developing streaming algorithms for these problems. Constant space algorithms are known…

We study first-order optimization algorithms under the constraint that the descent direction is quantized using a pre-specified budget of $R$-bits per dimension, where $R \in (0 ,\infty)$. We propose computationally efficient optimization…

This work investigates the nonparametric estimation of the vector field of a noisy Ordinary Differential Equation (ODE) in high-dimensional ambient spaces, under the assumption that the initial conditions are sampled from a…

We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…

Identifying meaningful signal buried in noise is a problem of interest arising in diverse scenarios of data-driven modeling. We present here a theoretical framework for exploiting intrinsic geometry in data that resists noise corruption,…