arXiv research

RL solves discrete LQ control with Gaussian optimal policy.

We introduce a Bernstein-type inequality which serves to uniformly control quadratic forms of gaussian variables. The latter can for example be used to derive sharp model selection criteria for linear estimation in linear regression and linear inverse problems via penalization, and we do not exclude that its scope of a…

LqgOpt learns optimal control in unknown LQG systems with minimal regret.

Gaussian equivalence fails for simple polynomial embeddings in quadratic scaling RF models.

The study sets limits on how well systems can be controlled adaptively.

We study the variance of the REINFORCE policy gradient estimator in environments with continuous state and action spaces, linear dynamics, quadratic cost, and Gaussian noise. These simple environments allow us to derive bounds on the estimator variance in terms of the environment and noise parameters. We compare the pr…

Study cost-driven state representation learning for control from partial observations.

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…

We study the performance of the certainty equivalent controller on Linear Quadratic (LQ) control problems with unknown transition dynamics. We show that for both the fully and partially observed settings, the sub-optimality gap between the cost incurred by playing the certainty equivalent controller on the true system …

Study learns state representations from observations for control, proving guarantees.

We provide explicit solutions of certain forward-backward stochastic differential equations (FBSDEs) with quadratic growth. These particular FBSDEs are associated with quadratic term structure models of interest rates and characterize the zero-coupon bond price. The results of this paper are naturally related to simila…

We explore a new method for discrete-time control problems using randomization and entropy.

Study capacity constraints in continual learning with a simple model.

New algorithm for learning causal structures with disjoint cycles in linear non-Gaussian models.

This tutorial explains Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) as two fundamental classification methods in statistical and probabilistic learning. We start with the optimization of decision boundary on which the posteriors are equal. Then, LDA and QDA are derived for binary and mul…

Optimal linear contracts are possible even with memory in Gaussian settings.

Faster algorithms for structured SVMs reduce computation time.

Gaussian surrogates improve Poisson imaging performance at low doses.

A Gaussian Process Ordinary Differential Equation framework for large continuous dynamical systems

Finding optimal feedback controllers for nonlinear dynamic systems from data is hard. Recently, Bayesian optimization (BO) has been proposed as a powerful framework for direct controller tuning from experimental trials. For selecting the next query point and finding the global optimum, BO relies on a probabilistic desc…

Ens-CGP synthesizes ensemble-based inference with Gaussian processes.

This work optimizes RL algorithms using entropy regularisation for continuous-time LQ problems.

Partition functions arise in a variety of settings, including conditional random fields, logistic regression, and latent gaussian models. In this paper, we consider semistochastic quadratic bound (SQB) methods for maximum likelihood inference based on partition function optimization. Batch methods based on the quadrati…

This paper presents a novel one-factor stochastic volatility model where the instantaneous volatility of the asset log-return is a diffusion with a quadratic drift and a linear dispersion function. The instantaneous volatility mean reverts around a constant level, with a speed of mean reversion that is affine in the in…

Robust Kalman filter for corrupted measurements.

New robust discriminant analysis for non-Gaussian data.

Classifies surfaces in hyperbolic space with constant Gaussian curvature.

We study the supervised learning problem under either of the following two models: (1) Feature vectors ${\boldsymbol x}_i$ are $d$-dimensional Gaussians and responses are $y_i = f_*({\boldsymbol x}_i)$ for $f_*$ an unknown quadratic function; (2) Feature vectors ${\boldsymbol x}_i$ are distributed as a mixture of two $…

Non-bilinear observations make optimal control harder, showing non-convex costs and non-affine optimal controllers.

Paper optimizes WGAN parameters for non-Gaussian data.

The paper models financial correlation matrices using permutation invariant Gaussian models and predicts market anomalies.

Paper analyzes holdout cross-validation for large non-Gaussian covariance estimation.

A new robust and flexible classification method for non-Gaussian data.

The paper models asset pricing in a partially observed market using mean field game theory and exponential quadratic Gaussian framework.

Paper tackles sim-to-real transfer in continuous domains with partial observations.

New algorithm for robust regression with subgaussian error bound.

The authors aim to develop numerical schemes of the two representative quadratic hedging strategies: locally risk minimizing and mean-variance hedging strategies, for models whose asset price process is given by the exponential of a normal inverse Gaussian process, using the results of Arai et al. \cite{AIS}, and Arai …

Study shows efficient algorithms for noiseless linear regression require quadratic sample complexity in contamination rate.

The statistical dependencies which independent component analysis (ICA) cannot remove often provide rich information beyond the linear independent components. It would thus be very useful to estimate the dependency structure from data. While such models have been proposed, they usually concentrated on higher-order corr…

New method improves efficiency of non-convex matrix reconstruction.

This paper aims at refined error analysis for binary classification using support vector machine (SVM) with Gaussian kernel and convex loss. Our first result shows that for some loss functions such as the truncated quadratic loss and quadratic loss, SVM with Gaussian kernel can reach the almost optimal learning rate, p…

This work improves Gaussian process model selection for large datasets.

Sparse Gaussian processes with compact kernels for faster inference.

Unified framework for robust discriminant analysis overcomes Gaussian assumptions.

Improved sample efficiency for private learning of Gaussian mixtures.

Paper proposes GPM for heteroscedastic PCA estimation.

Quantum algorithm speeds up Lasso regression by quadratically faster per iteration.

New bound matches exact generalization error for quadratic Gaussian problem.