arXiv research

New filters for non-linear systems achieve closed-form solutions.

New method for inferring time series graph from sparse-group log-sum penalty.

Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing

Paper introduces a new kernel model for PSD-valued functions with theoretical guarantees and applications.

In this paper, we study the prediction of a circularly symmetric zero-mean stationary Gaussian process from a window of observations consisting of finitely many samples. This is a prevalent problem in a wide range of applications in communication theory and signal processing. Due to stationarity, when the autocorrelati…

A new algorithm improves sampling for graph learning models.

Unified approach to Bayesian inference with guarantees on covariance matrices.

PSD models simplify probability density estimation.

New kernel handles irregularly-spaced multivariate time series.

Develops nonstationary MOGP kernels for better performance.

Rank-one measurements limit feasible sets for low-rank PSD matrices.

An algorithm for computing positive semidefinite factorizations of matrices.

New method infers graph from dependent matrix data.

New methods for sketching non-PSD matrices improve regression and optimization tasks.

A new method for assessing Bayesian sampling quality, PSD, is proposed and shown to be more powerful and efficient.

Several important applications, such as streaming PCA and semidefinite programming, involve a large-scale positive-semidefinite (psd) matrix that is presented as a sequence of linear updates. Because of storage limitations, it may only be possible to retain a sketch of the psd matrix. This paper develops a new algorith…

Machine learning uncovers hidden correlations in granular material behavior.

The paper analyzes Karcher means on restricted PSD matrices with statistical guarantees.

Improved covariance matrix estimation for portfolio optimization with guaranteed PSD and controlled conditioning.

We consider whether algorithmic choices in over-parameterized linear matrix factorization introduce implicit regularization. We focus on noiseless matrix sensing over rank-$r$ positive semi-definite (PSD) matrices in $\mathbb{R}^{n \times n}$, with a sensing mechanism that satisfies restricted isometry properties (RIP)…

This paper proposes an efficient method for sampling from stochastic differential equations using PSD models.

Bayesian optimization gains efficiency by leveraging symmetries through a modified max kernel.

We consider the problem of clustering noisy finite-length observations of stationary ergodic random processes according to their nonparametric generative models without prior knowledge of the model statistics and the number of generative models. Two algorithms, both using the L1-distance between estimated power spectra…

We consider the problem of clustering noisy finite-length observations of stationary ergodic random processes according to their generative models without prior knowledge of the model statistics and the number of generative models. Two algorithms, both using the $L^1$-distance between estimated power spectral densities…

Owing to small size, sensing capabilities and autonomous nature, the Unmanned Air Vehicles (UAVs) have enormous applications in various areas, e.g., remote sensing, navigation, archaeology, journalism, environmental science, and agriculture. However, the unmonitored deployment of UAVs called the amateur drones (AmDr) c…

Optimal sample complexity for learning DDAGs from noisy data.

Sparse graph learning for dependent time series using ADMM.

Power spectral density (PSD) maps providing the distribution of RF power across space and frequency are constructed using power measurements collected by a network of low-cost sensors. By introducing linear compression and quantization to a small number of bits, sensor measurements can be communicated to the fusion cen…

New algorithm helps escape saddle points in optimization problems.

Despite the success of the popular kernelized support vector machines, they have two major limitations: they are restricted to Positive Semi-Definite (PSD) kernels, and their training complexity scales at least quadratically with the size of the data. Many natural measures of similarity between pairs of samples are not…

A new imputation method estimates missing values by matching observed marginals from masked data.

ITSPACE improves covariance alignment faster than other methods.

Recurrent neural networks (RNNs) are a vital modeling technique that rely on internal states learned indirectly by optimization of a supervised, unsupervised, or reinforcement training loss. RNNs are used to model dynamic processes that are characterized by underlying latent states whose form is often unknown, precludi…

Efficient approximations reduce computation of matrix-based Renyi's entropy.

We consider online learning for minimizing regret in unknown, episodic Markov decision processes (MDPs) with continuous states and actions. We develop variants of the UCRL and posterior sampling algorithms that employ nonparametric Gaussian process priors to generalize across the state and action spaces. When the trans…

The paper presents two schemes for sampling matrices from specific distributions on a manifold.

Proposes a probabilistic framework for stationary topological signals on simplicial complexes.

We show that given an estimate $\widehat{A}$ that is close to a general high-rank positive semi-definite (PSD) matrix $A$ in spectral norm (i.e., $\|\widehat{A}-A\|_2 \leq δ$), the simple truncated SVD of $\widehat{A}$ produces a multiplicative approximation of $A$ in Frobenius norm. This observation leads to many inte…

Paper studies asymmetric matrix sensing, proving gradient descent converges to low-rank solutions.

New PSDMF algorithms derived from PR and ARM methods.

Complex embeddings handle non-metric proximity data better than traditional methods.

We consider the non-square matrix sensing problem, under restricted isometry property (RIP) assumptions. We focus on the non-convex formulation, where any rank-$r$ matrix $X \in \mathbb{R}^{m \times n}$ is represented as $UV^\top$, where $U \in \mathbb{R}^{m \times r}$ and $V \in \mathbb{R}^{n \times r}$. In this paper…

Equivalent formulations for low-rank matrix optimization are proven.

Simplified analysis of SGD for linear regression with weight averaging.

Scaled gradient descent improves matrix recovery for ill-conditioned matrices with optimal sampling complexity.

Variance reduction techniques like SVRG provide simple and fast algorithms for optimizing a convex finite-sum objective. For nonconvex objectives, these techniques can also find a first-order stationary point (with small gradient). However, in nonconvex optimization it is often crucial to find a second-order stationary…

We study the projected gradient descent method on low-rank matrix problems with a strongly convex objective. We use the Burer-Monteiro factorization approach to implicitly enforce low-rankness; such factorization introduces non-convexity in the objective. We focus on constraint sets that include both positive semi-defi…

RPCholesky approximates kernel matrices with few evaluations.