arXiv research

Paper improves efficiency in matrix computations for Gaussian processes.

IPGP framework improves psychological assessment by integrating shared and unique traits.

We add size factor to CAPM and normalize residuals by Volatility Index.

We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to depend on a set of globally relevant inducing variables which factorize the model …

Paper solves robust convex problems with heavy-tailed noise.

The paper improves boundary detection and density estimation on noisy data.

A scalable GPLVM model using stochastic variational inference.

We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence structure in the model. Incorporating sparsity in the precision matrix allows the Gaus…

Beta process is the standard nonparametric Bayesian prior for latent factor model. In this paper, we derive a structured mean-field variational inference algorithm for a beta process non-negative matrix factorization (NMF) model with Poisson likelihood. Unlike the linear Gaussian model, which is well-studied in the non…

New method predicts dynamic relationships in terrorist networks.

A new model fits SPX and VIX volatility surfaces and term structures efficiently.

This paper studies a continuous-time market {under stochastic environment} where an agent, having specified an investment horizon and a target terminal mean return, seeks to minimize the variance of the return with multiple stocks and a bond. In the considered model firstly proposed by [3], the mean returns of individu…

Improves BBVI for high-dimensional Gaussian approximations by using low-rank approximations.

Study compares two factor models for electricity spot prices across different periods.

While stochastic variational inference is relatively well known for scaling inference in Bayesian probabilistic models, related methods also offer ways to circumnavigate the approximation of analytically intractable expectations. The key challenge in either setting is controlling the variance of gradient estimates: rec…

We consider maximum likelihood estimation for Gaussian Mixture Models (Gmms). This task is almost invariably solved (in theory and practice) via the Expectation Maximization (EM) algorithm. EM owes its success to various factors, of which is its ability to fulfill positive definiteness constraints in closed form is of …

Proposes a nonparametric tensor factorization for sparse data.

Proposes a new Gaussian factor for probabilistic inference with degenerate settings.

Efficiently models Wrong-Way Risk in FVA without full Monte Carlo.

A new method for efficient Gaussian process inference using sparse approximations.

Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the approximate posterior in the hope of improving performance. In contrast, here we share a …

The paper tackles best arm identification in contaminated bandits with optimal error guarantees and sample complexity.

We introduce a multi-factor stochastic volatility model based on the CIR/Heston volatility process that incorporates seasonality and the Samuelson effect. First, we give conditions on the seasonal term under which the corresponding volatility factor is well-defined. These conditions appear to be rather mild. Second, we…

SGD with constant stepsize converges to a non-Gaussian limit near flat minima.

Improved SVI with adjustable annealing for better optimization.

Copulas have become an important tool in the modern best practice Enterprise Risk Management, often supplanting other approaches to modelling stochastic dependence. However, choosing the `right' copula is not an easy task, and the temptation to prefer a tractable rather than a meaningful candidate from the encompassing…

We analyze single-layer neural networks with the Xavier initialization in the asymptotic regime of large numbers of hidden units and large numbers of stochastic gradient descent training steps. The evolution of the neural network during training can be viewed as a stochastic system and, using techniques from stochastic…

Paper derives convergence rates and confidence intervals for LSA with Markovian noise.

New analysis shows SGD with noise doesn't leak more privacy with more iterations.

VNNGP uses nearest neighbors to approximate GPs, improving scalability and performance.

GCNs improve multi-layer network classification by expanding the distance between means.

Robustly infers manifold density and geometry under high-dimensional noise.

Efficiently simulates the Heston model with large time steps using a novel method.

Gaussian copulas are widely used in the industry to correlate two random variables when there is no prior knowledge about the co-dependence between them. The perturbed Gaussian copula approach allows introducing the skew information of both random variables into the co-dependence structure. The analytical expression of…

New findings show Gaussian universality breaks down in high-dimensional linear factor mixtures.

Study pricing options on forward contracts using infinite-dimensional affine models.

Efficiently learns deep factor graphs using Gaussian belief propagation.

Scalable Gaussian process models trained with unbiased stochastic ELBO.

Improved sample complexity for Gaussian Mixture Models using Pair Correlation Factor.

Paper revisits DP-SCO in Euclidean and $\ell_p^d$ spaces, focusing on constrained and bounded sets.

Nonnegative matrix factorization (NMF), a dimensionality reduction and factor analysis method, is a special case in which factor matrices have low-rank nonnegative constraints. Considering the stochastic learning in NMF, we specifically address the multiplicative update (MU) rule, which is the most popular, but which h…

The recent financial crisis has led to so-called multi-curve models for the term structure. Here we study a multi-curve extension of short rate models where, in addition to the short rate itself, we introduce short rate spreads. In particular, we consider a Gaussian factor model where the short rate and the spreads are…

Authors improve accuracy analysis for portfolio optimization with multiple timescale factors.

We propose a fast algorithm for computing the expected tranche loss in the Gaussian factor model. We test it on a 125 name portfolio with a single factor Gaussian model and show that the algorithm gives accurate results. We choose a 125 name portfolio for our tests because this is the size of the standard DJCDX.NA.HY p…

A scalable factorized Gaussian process VAE for faster inference.

This paper tackles robust growth maximization with stochastic factors, finding optimal strategies independent of the factor process.

Improved growth strategies by incorporating stochastic factors in asset returns.

Heteroscedastic regression considering the varying noises among observations has many applications in the fields like machine learning and statistics. Here we focus on the heteroscedastic Gaussian process (HGP) regression which integrates the latent function and the noise function together in a unified non-parametric B…