Fitting Jump Models

We describe a new framework for fitting jump models to a sequence of data. The key idea is to alternate between minimizing a loss function to fit multiple model parameters, and minimizing a discrete loss function to determine which set of model parameters is active at each data point. The framework is quite general and encompasses popular classes of models, such as hidden Markov models and piecewise affine models. The shape of the chosen loss functions to minimize determine the shape of the resulting jump model.Comment: Accepted for publication in Automatic

Model-Based Reinforcement Learning for Stochastic Hybrid Systems

Optimal control of general nonlinear systems is a central challenge in automation. Enabled by powerful function approximators, data-driven approaches to control have recently successfully tackled challenging robotic applications. However, such methods often obscure the structure of dynamics and control behind black-box over-parameterized representations, thus limiting our ability to understand closed-loop behavior. This paper adopts a hybrid-system view of nonlinear modeling and control that lends an explicit hierarchical structure to the problem and breaks down complex dynamics into simpler localized units. We consider a sequence modeling paradigm that captures the temporal structure of the data and derive an expectation-maximization (EM) algorithm that automatically decomposes nonlinear dynamics into stochastic piecewise affine dynamical systems with nonlinear boundaries. Furthermore, we show that these time-series models naturally admit a closed-loop extension that we use to extract local polynomial feedback controllers from nonlinear experts via behavioral cloning. Finally, we introduce a novel hybrid relative entropy policy search (Hb-REPS) technique that incorporates the hierarchical nature of hybrid systems and optimizes a set of time-invariant local feedback controllers derived from a local polynomial approximation of a global state-value function

Time of day effects of temperature and daylight on short term electricity load

This paper proposes a model for short-term electricity load with differentiated temperature and daylight effects by time of day, which are determined by variations in intraday economic activity. The relationship between electricity load and economic activity implies that the electricity demand response to changes in exogenous variables like temperature is non-linear as well as non-homogeneous along the day. The proposed framework, a smooth transition regression model with double threshold (LSTR2), models the observed intraday patterns in load curves to explicitly capture the effect of the circadian rest-activity cycle on the distinct responses of electricity demand to temperature and daylight variations throughout the day. The model shows that the sensitivity of demand to low temperatures is significantly larger in the “active” compared to the “rest” state. If temperatures decrease from 10 °C to 0 °C, electricity demand in the “active” state increases by 960.5 MW h per 1 °C decrease, but by only 26.6 MW h per 1 °C decrease in the “rest” state. When temperatures are higher, in the “rest state” demand decreases by 602.9 MW h per 1 °C if temperature falls from 26 °C to 21 °C, while in the “active” state demand only decreases by 323.6 MW h per 1 °C variatio

Improved very short-term spatio-temporal wind forecasting using atmospheric regimes

We present a regime‐switching vector autoregressive method for very short‐term wind speed forecasting at multiple locations with regimes based on large‐scale meteorological phenomena. Statistical methods for wind speed forecasting based on recent observations outperform numerical weather prediction for forecast horizons up to a few hours, and the spatio‐temporal interdependency between geographically dispersed locations may be exploited to improve forecast skill. Here, we show that conditioning spatio‐temporal interdependency on “atmospheric modes” derived from gridded numerical weather data can further improve forecast performance. Atmospheric modes are based on the clustering of surface wind and sea‐level pressure fields, and the geopotential height field at the 5000‐hPa level. The data fields are extracted from the MERRA‐2 reanalysis dataset with an hourly temporal resolution over the UK; atmospheric patterns are clustered using self‐organising maps and then grouped further to optimise forecast performance. In a case study based on 6 years of measurements from 23 weather stations in the UK, a set of 3 atmospheric modes are found to be optimal for forecast performance. The skill of 1‐ to 6‐hour‐ahead forecasts is improved at all sites compared with persistence and competitive benchmarks. Across the 23 test sites, 1‐hour‐ahead root mean squared error is reduced by between 0.3% and 4.1% compared with the best performing benchmark and by an average of 1.6% over all sites; the 6‐hour‐ahead accuracy is improved by an average of 3.1%

Identification des régimes et regroupement des séquences pour la prévision des marchés financiers

Abstract : Regime switching analysis is extensively advocated to capture complex behaviors underlying financial time series for market prediction. Two main disadvantages in current approaches of regime identification are raised in the literature: 1) the lack of a mechanism for identifying regimes dynamically, restricting them to switching among a fixed set of regimes with a static transition probability matrix; 2) failure to utilize cross-sectional regime dependencies among time series, since not all the time series are synchronized to the same regime. As the numerical time series can be symbolized into categorical sequences, a third issue raises: 3) the lack of a meaningful and effective measure of the similarity between chronological dependent categorical values, in order to identify sequence clusters that could serve as regimes for market forecasting. In this thesis, we propose a dynamic regime identification model that can identify regimes dynamically with a time-varying transition probability, to address the first issue. For the second issue, we propose a cluster-based regime identification model to account for the cross-sectional regime dependencies underlying financial time series for market forecasting. For the last issue, we develop a dynamic order Markov model, making use of information underlying frequent consecutive patterns and sparse patterns, to identify the clusters that could serve as regimes identified on categorized financial time series. Experiments on synthetic and real-world datasets show that our two regime models show good performance on both regime identification and forecasting, while our dynamic order Markov clustering model also demonstrates good performance on identifying clusters from categorical sequences.L'analyse de changement de régime est largement préconisée pour capturer les comportements complexes sous-jacents aux séries chronologiques financières pour la prédiction du marché. Deux principaux problèmes des approches actuelles d'identifica-tion de régime sont soulevés dans la littérature. Il s’agit de: 1) l'absence d'un mécanisme d'identification dynamique des régimes. Ceci limite la commutation entre un ensemble fixe de régimes avec une matrice de probabilité de transition statique; 2) l’incapacité à utiliser les dépendances transversales des régimes entre les séries chronologiques, car toutes les séries chronologiques ne sont pas synchronisées sur le même régime. Étant donné que les séries temporelles numériques peuvent être symbolisées en séquences catégorielles, un troisième problème se pose: 3) l'absence d'une mesure significative et efficace de la similarité entre les séries chronologiques dépendant des valeurs catégorielles pour identifier les clusters de séquences qui pourraient servir de régimes de prévision du marché. Dans cette thèse, nous proposons un modèle d'identification de régime dynamique qui identifie dynamiquement des régimes avec une probabilité de transition variable dans le temps afin de répondre au premier problème. Ensuite, pour adresser le deuxième problème, nous proposons un modèle d'identification de régime basé sur les clusters. Notre modèle considère les dépendances transversales des régimes sous-jacents aux séries chronologiques financières avant d’effectuer la prévision du marché. Pour terminer, nous abordons le troisième problème en développant un modèle de Markov d'ordre dynamique, en utilisant les informations sous-jacentes aux motifs consécutifs fréquents et aux motifs clairsemés, pour identifier les clusters qui peuvent servir de régimes identifiés sur des séries chronologiques financières catégorisées. Nous avons mené des expériences sur des ensembles de données synthétiques et du monde réel. Nous démontrons que nos deux modèles de régime présentent de bonnes performances à la fois en termes d'identification et de prévision de régime, et notre modèle de clustering de Markov d'ordre dynamique produit également de bonnes performances dans l'identification de clusters à partir de séquences catégorielles