Related papers: Predicting path-dependent processes by deep learni…

Causal discovery from empirical data is a fundamental problem in many scientific domains. Observational data allows for identifiability only up to Markov equivalence class. In this paper we first propose a polynomial time algorithm for…

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…

Choice modeling has been a central topic in the study of individual preference or utility across many fields including economics, marketing, operations research, and psychology. While the vast majority of the literature on choice models has…

Fractional Ornstein-Uhlenbeck process of the second kind $(\text{fOU}_{2})$ is solution of the Langevin equation $\mathrm{d}X_t = -\theta X_t\,\mathrm{d}t+\mathrm{d}Y_t^{(1)}, \ \theta >0$ with Gaussian driving noise $ Y_t^{(1)} := \int^t_0…

Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a…

We review the application of Statistical Mechanics methods to the study of online learning of a drifting concept in the limit of large systems. The model where a feed-forward network learns from examples generated by a time dependent…

Accurate traffic participant prediction is the prerequisite for collision avoidance of autonomous vehicles. In this work, we predict pedestrians by emulating their own motion planning. From online observations, we infer a mixture density…

Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…

Quantifying predictive uncertainty of deep semantic segmentation networks is essential in safety-critical tasks. In applications like autonomous driving, where video data is available, convolutional long short-term memory networks are…

We develop a (nearly) unbiased particle filtering algorithm for a specific class of continuous-time state-space models, such that (a) the latent process $X_t$ is a linear Gaussian diffusion; and (b) the observations arise from a Poisson…

We study nonlinear regression of real valued data in an individual sequence manner, where we provide results that are guaranteed to hold without any statistical assumptions. We address the convergence and undertraining issues of…

We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…

Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…

The modeling of realistic magnetic materials requires the inclusion of defects. Based on the pseudospectral Landau-Lifshitz description of magnetisation dynamics, we propose a statistical model that takes into account defects, specifically…

Tipping points occur in many real-world systems, at which the system shifts suddenly from one state to another. The ability to predict the occurrence of tipping points from time series data remains an outstanding challenge and a major…

We address the problem of prediction of multivariate data process using an underlying graph model. We develop a method that learns a sparse partial correlation graph in a tuning-free and computationally efficient manner. Specifically, the…

Branch prediction is an architectural feature that speeds up the execution of branch instruction on pipeline processors and reduces the cost of branching. Recent advancements of Deep Learning (DL) in the post Moore's Law era is accelerating…

We consider Langevin equation involving fractional Brownian motion with Hurst index $H\in(0,\frac12)$. Its solution is the fractional Ornstein-Uhlenbeck process and with unknown drift parameter $\theta$. We construct the estimator that is…

We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…

The Path-Dependent Neural Jump Ordinary Differential Equation (PD-NJ-ODE) is a model for predicting continuous-time stochastic processes with irregular and incomplete observations. In particular, the method learns optimal forecasts given…