Mixture-Based Clustering and Hidden Markov Models for Energy Management and Human Activity Recognition: Novel Approaches and Explainable Applications

In recent times, the rapid growth of data in various fields of life has created an immense need for powerful tools to extract useful information from data. This has motivated researchers to explore and devise new ideas and methods in the field of machine learning. Mixture models have gained substantial attention due to their ability to handle high-dimensional data efficiently and effectively. However, when adopting mixture models in such spaces, four crucial issues must be addressed, including the selection of probability density functions, estimation of mixture parameters, automatic determination of the number of components, identification of features that best discriminate the different components, and taking into account the temporal information. The primary objective of this thesis is to propose a unified model that addresses these interrelated problems. Moreover, this thesis proposes a novel approach that incorporates explainability. This thesis presents innovative mixture-based modelling approaches tailored for diverse applications, such as household energy consumption characterization, energy demand management, fault detection and diagnosis and human activity recognition. The primary contributions of this thesis encompass the following aspects: Initially, we propose an unsupervised feature selection approach embedded within a finite bounded asymmetric generalized Gaussian mixture model. This model is adept at handling synthetic and real-life smart meter data, utilizing three distinct feature extraction methods. By employing the expectation-maximization algorithm in conjunction with the minimum message length criterion, we are able to concurrently estimate the model parameters, perform model selection, and execute feature selection. This unified optimization process facilitates the identification of household electricity consumption profiles along with the optimal subset of attributes defining each profile. Furthermore, we investigate the impact of household characteristics on electricity usage patterns to pinpoint households that are ideal candidates for demand reduction initiatives. Subsequently, we introduce a semi-supervised learning approach for the mixture of mixtures of bounded asymmetric generalized Gaussian and uniform distributions. The integration of the uniform distribution within the inner mixture bolsters the model's resilience to outliers. In the unsupervised learning approach, the minimum message length criterion is utilized to ascertain the optimal number of mixture components. The proposed models are validated through a range of applications, including chiller fault detection and diagnosis, occupancy estimation, and energy consumption characterization. Additionally, we incorporate explainability into our models and establish a moderate trade-off between prediction accuracy and interpretability. Finally, we devise four novel models for human activity recognition (HAR): bounded asymmetric generalized Gaussian mixture-based hidden Markov model with feature selection~(BAGGM-FSHMM), bounded asymmetric generalized Gaussian mixture-based hidden Markov model~(BAGGM-HMM), asymmetric generalized Gaussian mixture-based hidden Markov model with feature selection~(AGGM-FSHMM), and asymmetric generalized Gaussian mixture-based hidden Markov model~(AGGM-HMM). We develop an innovative method for simultaneous estimation of feature saliencies and model parameters in BAGGM-FSHMM and AGGM-FSHMM while integrating the bounded support asymmetric generalized Gaussian distribution~(BAGGD), the asymmetric generalized Gaussian distribution~(AGGD) in the BAGGM-HMM and AGGM-HMM respectively. The aforementioned proposed models are validated using video-based and sensor-based HAR applications, showcasing their superiority over several mixture-based hidden Markov models~(HMMs) across various performance metrics. We demonstrate that the independent incorporation of feature selection and bounded support distribution in a HAR system yields benefits; Simultaneously, combining both concepts results in the most effective model among the proposed models

A novel dynamic asset allocation system using Feature Saliency Hidden Markov models for smart beta investing

The financial crisis of 2008 generated interest in more transparent, rules-based strategies for portfolio construction, with Smart beta strategies emerging as a trend among institutional investors. While they perform well in the long run, these strategies often suffer from severe short-term drawdown (peak-to-trough decline) with fluctuating performance across cycles. To address cyclicality and underperformance, we build a dynamic asset allocation system using Hidden Markov Models (HMMs). We test our system across multiple combinations of smart beta strategies and the resulting portfolios show an improvement in risk-adjusted returns, especially on more return oriented portfolios (up to 50$\%$ in excess of market annually). In addition, we propose a novel smart beta allocation system based on the Feature Saliency HMM (FSHMM) algorithm that performs feature selection simultaneously with the training of the HMM, to improve regime identification. We evaluate our systematic trading system with real life assets using MSCI indices; further, the results (up to 60$\%$ in excess of market annually) show model performance improvement with respect to portfolios built using full feature HMMs

Hierarchically-coupled hidden Markov models for learning kinetic rates from single-molecule data

We address the problem of analyzing sets of noisy time-varying signals that all report on the same process but confound straightforward analyses due to complex inter-signal heterogeneities and measurement artifacts. In particular we consider single-molecule experiments which indirectly measure the distinct steps in a biomolecular process via observations of noisy time-dependent signals such as a fluorescence intensity or bead position. Straightforward hidden Markov model (HMM) analyses attempt to characterize such processes in terms of a set of conformational states, the transitions that can occur between these states, and the associated rates at which those transitions occur; but require ad-hoc post-processing steps to combine multiple signals. Here we develop a hierarchically coupled HMM that allows experimentalists to deal with inter-signal variability in a principled and automatic way. Our approach is a generalized expectation maximization hyperparameter point estimation procedure with variational Bayes at the level of individual time series that learns an single interpretable representation of the overall data generating process.Comment: 9 pages, 5 figure

A Nonparametric Bayesian Approach to Uncovering Rat Hippocampal Population Codes During Spatial Navigation

Rodent hippocampal population codes represent important spatial information about the environment during navigation. Several computational methods have been developed to uncover the neural representation of spatial topology embedded in rodent hippocampal ensemble spike activity. Here we extend our previous work and propose a nonparametric Bayesian approach to infer rat hippocampal population codes during spatial navigation. To tackle the model selection problem, we leverage a nonparametric Bayesian model. Specifically, to analyze rat hippocampal ensemble spiking activity, we apply a hierarchical Dirichlet process-hidden Markov model (HDP-HMM) using two Bayesian inference methods, one based on Markov chain Monte Carlo (MCMC) and the other based on variational Bayes (VB). We demonstrate the effectiveness of our Bayesian approaches on recordings from a freely-behaving rat navigating in an open field environment. We find that MCMC-based inference with Hamiltonian Monte Carlo (HMC) hyperparameter sampling is flexible and efficient, and outperforms VB and MCMC approaches with hyperparameters set by empirical Bayes