arXiv research

PALS extends PAL for optimizing stochastic simulators efficiently.

Gaussian Process Factor Analysis (GPFA) has been broadly applied to the problem of identifying smooth, low-dimensional temporal structure underlying large-scale neural recordings. However, spike trains are non-Gaussian, which motivates combining GPFA with discrete observation models for binned spike count data. The dra…

Lapse improves parameter servers by dynamically allocating parameters, achieving near-linear scaling.

Study predicts lens performance using neural networks.

Multi-task learning shares information between related tasks, sometimes reducing the number of parameters required. State-of-the-art results across multiple natural language understanding tasks in the GLUE benchmark have previously used transfer from a single large task: unsupervised pre-training with BERT, where a sep…

Algorithm identifies Pareto optimal designs efficiently for noisy, multi-objective functions.

Squint bound improved by removing $\ln \ln T$ term.

Gradient descent optimization improved by circuit perspective.

We study a mean-field version of rank-based models of equity markets such as the Atlas model introduced by Fernholz in the framework of Stochastic Portfolio Theory. We obtain an asymptotic description of the market when the number of companies grows to infinity. Then, we discuss the long-term capital distribution. We r…

New equations reveal how cylinder power in progressive lenses depends on geodesic curvature.

We introduce a new system of stochastic differential equations which models dependence of market beta and unsystematic risk upon size, measured by market capitalization. We fit our model using size deciles data from Kenneth French's data library. This model is somewhat similar to generalized volatility-stabilized model…

In his seminal work \cite{pal:61}, R. Palais extended a substantial part of the theory of compact transformation groups to the case of proper actions of locally compact groups. Here we extend to proper actions some other important results well known for compact group actions. In particular, we prove that if $H$ is a co…

We introduce a formal language IE that is a variant of the language PAL developed in [van Benthem 2011] by adding a belief operator and a common belief operator,specializing to stochastic analysis. A constant symbol in the language denotes a stochastic process so that we can represent several financial events as formul…

Boolean matrix factorization (BMF) is a popular and powerful technique for inferring knowledge from data. The mining result is the Boolean product of two matrices, approximating the input dataset. The Boolean product is a disjunction of rank-1 binary matrices, each describing a feature-relation, called pattern, for a g…

New algorithm learns multiclass concepts with finite Littlestone dimension.

Proposes a new method combining Reservoir Computing and Normalizing Flow for predicting stochastic dynamical systems.

The paper studies stochastic optimization on matrices and its limits as dimensions grow.

Study laws of large numbers in online classification, determining optimal regret bounds.

Efficiently estimates optimal transport maps with rigorous guarantees.

Improved mistake bound for group linear separable cases in online multiclass linear classification.

Optimal transport and information geometry both study geometric structures on spaces of probability distributions. Optimal transport characterizes the cost-minimizing movement from one distribution to another, while information geometry originates from coordinate-invariant properties of statistical inference. Their con…

Let $X$ and $Y$ be domains of $\mathbb{R}^n$ equipped with respective probability measures $μ$ and $ν$. We consider the problem of optimal transport from $μ$ to $ν$ with respect to a cost function $c: X \times Y \to \mathbb{R}$. To ensure that the solution to this problem is smooth, it is necessary to make several ass…