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The predictive quality of machine learning models is typically measured in terms of their (approximate) expected prediction accuracy or the so-called Area Under the Curve (AUC). Minimizing the reciprocals of these measures are the goals of…
Weak consistency and asymptotic normality of the ordinary least-squares estimator in a linear regression with adaptive learning is derived when the crucial, so-called, `gain' parameter is estimated in a first step by nonlinear least squares…
Financial markets are highly complex and volatile; thus, learning about such markets for the sake of making predictions is vital to make early alerts about crashes and subsequent recoveries. People have been using learning tools from…
Recent research has challenged the necessity of complex deep learning architectures for time series forecasting, demonstrating that simple linear models can often outperform sophisticated approaches. Building upon this insight, we introduce…
We introduce Temporal Variational Implicit Neural Representations (TV-INRs), a probabilistic framework for modeling irregular multivariate time series that enables efficient individualized imputation and forecasting. By integrating implicit…
We consider the problem of the construction of the estimator-process of the unknown finite-dimensional parameter in the case of the observations of nonlinear autoregressive process. The estimation is done in two or three steps. First we…
Given a finite metric space $(X\cup Y, \mathbf{d})$ the $k$-median problem is to find a set of $k$ centers $C\subseteq Y$ that minimizes $\sum_{p\in X} \min_{c\in C} \mathbf{d}(p,c)$. In general metrics, the best polynomial time algorithm…
We aim at improving reasoning on inconsistent and uncertain data. We focus on knowledge-graph data, extended with time intervals to specify their validity, as regularly found in historical sciences. We propose principles on semantics for…
In transfer learning, the learner leverages auxiliary data to improve generalization on a main task. However, the precise theoretical understanding of when and how auxiliary data help remains incomplete. We provide new insights on this…
Probabilistic forecasting of high dimensional multivariate time series is a notoriously challenging task, both in terms of computational burden and distribution modeling. Most previous work either makes simple distribution assumptions or…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
Multivariate time series forecasting is a crucial task that predicts the future states based on historical inputs. Related techniques have been developing in parallel with the machine learning community, from early statistical learning…
In this paper, approximate Linear Minimum Variance (LMV) filters for continuous-discrete state space models are introduced. The filters are obtained by means of a recursive approximation to the predictions for the first two moments of the…
For a broad class of nonlinear time series known as Bernoulli shifts, we establish the asymptotic normality of the smoothed periodogram estimator of the long-run variance. This estimator uses only a narrow band of Fourier frequencies around…
The focus of this paper is on trend estimation for a general state-space model $Y_t=\mu_t+\varepsilon_t$, where the $d$th difference of the trend $\{\mu_t\}$ is assumed to be i.i.d., and the error sequence $\{\varepsilon_t\}$ is assumed to…
We study reinforcement learning methods with linear function approximation under non-Markov state and cost processes. We first consider the policy evaluation method and show that the algorithm converges under suitable ergodicity conditions…
In this paper we survey the most recent advances in supervised machine learning and high-dimensional models for time series forecasting. We consider both linear and nonlinear alternatives. Among the linear methods we pay special attention…
In this short note, we provide a sample complexity lower bound for learning linear predictors with respect to the squared loss. Our focus is on an agnostic setting, where no assumptions are made on the data distribution. This contrasts with…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
This paper considers a general class of parameter-driven models for time series of counts. A comprehensive simulation study is conducted to evaluate the accuracy and efficiency of three estimators: the maximum likelihood estimators of the…