Related papers: Fast multivariate empirical cumulative distributio…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
Divide-and-conquer is a general strategy to deal with large scale problems. It is typically applied to generate ensemble instances, which potentially limits the problem size it can handle. Additionally, the data are often divided by random…
Nuclear energy density functionals (EDFs) have a long history of success in reproducing properties of nuclei across the table of the nuclides. They capture quantitatively the emergent features of bound nuclei, such as nuclear saturation and…
In this paper, we provide faster algorithms for computing various fundamental quantities associated with random walks on a directed graph, including the stationary distribution, personalized PageRank vectors, hitting times, and escape…
We propose a novel deterministic sampling method to approximate a target distribution $\rho^*$ by minimizing the kernel discrepancy, also known as the Maximum Mean Discrepancy (MMD). By employing the general \emph{energetic variational…
Multi-dimensional distributions of discrete data that resemble ellipsoids arise in numerous areas of science, statistics, and computational geometry. We describe a complete algebraic algorithm to determine the quadratic form specifying the…
Orthogonal systems in $\mathrm{L}_2(\mathbb{R})$, once implemented in spectral methods, enjoy a number of important advantages if their differentiation matrix is skew-symmetric and highly structured. Such systems, where the differentiation…
We consider the Kalman-filtering problem with multiple sensors which are connected through a communication network. If all measurements are delivered to one place called fusion center and processed together, we call the process centralized…
In this paper, we show that efficient separated sum-of-exponentials approximations can be constructed for the heat kernel in any dimension. In one space dimension, the heat kernel admits an approximation involving a number of terms that is…
The family of Expectation-Maximization (EM) algorithms provides a general approach to fitting flexible models for large and complex data. The expectation (E) step of EM-type algorithms is time-consuming in massive data applications because…
Learning robot policies that capture multimodality in the training data has been a long-standing open challenge for behavior cloning. Recent approaches tackle the problem by modeling the conditional action distribution with generative…
In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more…
Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher order…
It is well known that, using fast algorithms for polynomial multiplication and division, evaluation of a polynomial $F \in \mathbb{C}[x]$ of degree $n$ at $n$ complex-valued points can be done with $\tilde{O}(n)$ exact field operations in…
We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above…
A number of methods have been proposed for causal effect estimation, yet few have demonstrated efficacy in handling data with complex structures, such as images. To fill this gap, we propose Causal Multi-task Deep Ensemble (CMDE), a novel…
In this work, we investigate dispersion interactions in a selection of atomic, molecular, and molecule-surface systems, comparing high-level correlated methods with empirically-corrected density functional theory (DFT). We assess the…
Multiple kernel learning algorithms are proposed to combine kernels in order to obtain a better similarity measure or to integrate feature representations coming from different data sources. Most of the previous research on such methods is…
Reinforcement learning often needs to deal with the exponential growth of states and actions when exploring optimal control in high-dimensional spaces (often known as the curse of dimensionality). In this work, we address this issue by…
Imbalanced response variable distribution is a common occurrence in data science. In fields such as fraud detection, medical diagnostics, system intrusion detection and many others where abnormal behavior is rarely observed the data under…