A Functional Wavelet-Kernel Approach for Continuous-time Prediction

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 observations are segments of the observed process considered as curves. These curves are assumed to lie within a space of possibly inhomogeneous functions, and the discretized times series dataset consists of a relatively small, compared to the number of segments, number of measurements made at regular times. We thus consider only the case where an asymptotically non-increasing number of measurements is available for each portion of the times series. We estimate conditional expectations using appropriate wavelet decompositions of the segmented sample paths. A notion of similarity, based on wavelet decompositions, is used in order to calibrate the prediction. Asymptotic properties when the number of segments grows to infinity are investigated under mild conditions, and a nonparametric resampling procedure is used to generate, in a flexible way, valid asymptotic pointwise confidence intervals for the predicted trajectories. We illustrate the usefulness of the proposed functional wavelet-kernel methodology in finite sample situations by means of three real-life datasets that were collected from different arenas

Adaptive Asynchronous Control Using Meta-learned Neural Ordinary Differential Equations

Model-based Reinforcement Learning and Control have demonstrated great potential in various sequential decision making problem domains, including in robotics settings. However, real-world robotics systems often present challenges that limit the applicability of those methods. In particular, we note two problems that jointly happen in many industrial systems: 1) Irregular/asynchronous observations and actions and 2) Dramatic changes in environment dynamics from an episode to another (e.g. varying payload inertial properties). We propose a general framework that overcomes those difficulties by meta-learning adaptive dynamics models for continuous-time prediction and control. The proposed approach is task-agnostic and can be adapted to new tasks in a straight-forward manner. We present evaluations in two different robot simulations and on a real industrial robot.Comment: 16 double column pages, 14 figures, 3 table

Power spectral density of a single Brownian trajectory: what one can and cannot learn from it

The power spectral density (PSD) of any time-dependent stochastic processXt is ameaningful feature of its spectral content. In its text-book definition, the PSD is the Fourier transform of the covariance function of Xt over an infinitely large observation timeT, that is, it is defined as an ensemble-averaged property taken in the limitT  ¥.Alegitimate question iswhat information on the PSDcan be reliably obtained from single-trajectory experiments, if one goes beyond the standard definition and analyzes thePSD of a single trajectory recorded for a finite observation timeT. In quest for this answer, for a d-dimensionalBrownian motion (BM) we calculate the probability density function of a single-trajectory PSDfor arbitrary frequency f, finite observation timeTand arbitrary number k of projections of the trajectory on different axes.We show analytically that the scaling exponent for the frequency-dependence of the PSDspecific to an ensemble ofBMtrajectories can be already obtained from a single trajectory, while the numerical amplitude in the relation between the ensemble-averaged and single-trajectory PSDs is afluctuating property which varies from realization to realization. The distribution of this amplitude is calculated exactly and is discussed in detail.Our results are confirmed by numerical simulations and single-particle tracking experiments, with remarkably good agreement. In addition we consider a truncatedWiener representation ofBM, and the case of a discrete-time lattice randomwalk.Wehighlight some differences in the behavior of a single-trajectory PSDforBMand for the two latter situations.The framework developed herein will allow formeaningful physical analysis of experimental stochastic trajectories

Reduction of discrete-time two-channel delayed systems

In this letter, the reduction method is extended to time-delay systems affected by two mismatched input delays. To this end, the intrinsic feedback structure of the retarded dynamics is exploited to deduce a reduced dynamics which is free of delays. Moreover, among other possibilities, an Immersion and Invariance feedback over the reduced dynamics is designed for achieving stabilization of the original systems. A chained sampled-data dynamics is used to show the effectiveness of the proposed control strategy through simulations

Short-Term Load Forecasting: The Similar Shape Functional Time Series Predictor

We introduce a novel functional time series methodology for short-term load forecasting. The prediction is performed by means of a weighted average of past daily load segments, the shape of which is similar to the expected shape of the load segment to be predicted. The past load segments are identified from the available history of the observed load segments by means of their closeness to a so-called reference load segment, the later being selected in a manner that captures the expected qualitative and quantitative characteristics of the load segment to be predicted. Weak consistency of the suggested functional similar shape predictor is established. As an illustration, we apply the suggested functional time series forecasting methodology to historical daily load data in Cyprus and compare its performance to that of a recently proposed alternative functional time series methodology for short-term load forecasting.Comment: 22 pages, 6 Figures, 1 Tabl