Contributions to the Estimation of Mixed-State Conditionally Heteroscedastic Latent Factor Models: A Comparative Study

Latent factor (LF) models are highly effective in extracting useful knowledge from High-Dimensional and Sparse (HiDS) matrices which are commonly seen in various industrial applications. An LF model usually adopts iterative optimizers, which may consume many iterations to achieve a local optima, resulting in considerable time cost. Hence, how to accelerate the training process of an LF model becomes a highly significant issue. To address it, this work innovatively proposes a randomized latent factor (RLF) model. It incorporates the principle of randomized learning techniques for neural networks into the LF analysis on HiDS matrices to alleviate the computational burden greatly. It also extends the standard learning process for randomized neural networks in context of LF analysis to make the resulting model represent an HiDS matrix correctly. Experimental results on three HiDS matrices from industrial applications demonstrate that compared with state-of-the-art LF models, RLF is able to achieve significantly higher computational efficiency and comparable prediction accuracy for missing data. More importantly, it provides a novel, effective, and efficient approach to LF analysis on HiDS matrices.

The human figure exhibits complex and rich dynamic behavior that is both nonlinear and time-varying. To automate the process of motion modeling we consider a class of learned dynamic models cast in the framework of dynamic Bayesian networks (DBNs) applied to analysis and tracking of the human figure. While direct learning of DBN parameters is possible, Bayesian learning formalism suggests that hyperparametric model description that considers all possible model dynamics may be preferred. Such integration over all possible models results in a subspace embedding of the original motion measurements. To this end, we propose a new family of Marginal Auto-Regressive (MAR) graphical models that describe the space of all stable auto-regressive sequences, regardless of their specific dynamics. We show that the use of dynamics and MAR models may lead to better estimates of sequence subspaces than the ones obtained by traditional non-sequential methods. We then propose a learning method for estimating general nonlinear dynamic system models that utilizes the new MAR models. The utility of the proposed methods is tested on the task of tracking 3D articulated figures in monocular image sequences. We demonstrate that the use of MAR can result in efficient and accurate tracking of the human figure from ambiguous visual inputs.

Buildings are subject to faults in their heating, ventilation and air-conditioning (HVAC) systems that can lead to excessive energy wastage, poor indoor climate, equipment failures and high maintenance costs. Field studies have shown that employing fault detection, diagnosis and prognosis (FDDP) tools followed up with equipment services and corrections can help achieve up to 40% of energy savings within the HVAC system and improve indoor climate, increase equipment lifecycle and reduce maintenance costs. The increasing adoption of building automation systems (BAS), Internet of Things (IoT) and other smart technologies in recent years have allowed large amounts of data to be continuously collected from building systems. This data-rich environment, along with the surge in data analytics and machine learning tools, has made cost-effective data-driven FDDP strategies possible. Compared to purely physics-based methods, data-driven methods require less explicit knowledge of the underlying physical system, thus are often easier to develop, and can learn certain intricate relationships that exist among data. Within the reported data-driven FDDP methods, there exists a few research gaps: 1) data imputation methods that leverage mutual information from correlated measurements to defy poor data quality from BAS have not been utilized efficiently; 2) there lacks a systematic and scalable fault diagnosis framework that incorporates probabilistic temporal relationships to track fault evolution; 3) existing fault diagnosis strategies typically focus on traditional rule-based control strategies and their scalability for advanced control strategies such as Guideline 36 have not been explored yet; 4) active threats information such as cyber-attacks, are typically not incorporated in an FDDP framework; 5) fault prognosis strategies to preemptively identify gradual faults for predictive maintenance have rarely been studied. This research attempts to address the above-mentioned research gaps through the following: Data Imputation: reported data imputation methods that are suitable for handling and repairing multi-source BAS data are evaluated. Data collected from a medium-sized, mixed-use institution building situated in Stockholm, Sweden and a small commercial building simulated in a laboratory setup is used to evaluate five different data imputation methods. Results demonstrate that incorporating time-lagged cross-correlations within the k-Nearest Neighbor (kNN) method helps to significantly improve the imputation accuracy and minimize the impact of repaired data on data-driven algorithms. Dynamic Bayesian Network (DBN)-based Framework for Cyber-Physical Fault Diagnosis: a DBN framework with discretized conditional probabilities parameters to represent the temporal relationships among building measurements is developed. Both domain knowledge and machine learning methods are used to develop the DBN structure and parameter model. The developed framework is evaluated for both traditional rule-based and Guideline 36 controls using datasets from a real building, a laboratory building, and a virtual testbed. Results show that the developed DBN framework is effective in diagnosing and isolating faults in systems even with different control strategies. The framework also successfully distinguishes whether system abnormalities originate from cyber-attacks or naturally occurring physical faults. Potential future direction to improve fault isolation using modified DBN topological structure is also reported in this study. DBN-based Framework for Fault Prognosis: an extension of the DBN framework in conjunction with Robust Multivariate Temporal (RMT) variate selection is proposed for fault prognosis. The RMT variate selection is used to extract localized temporal features from high dimensional datasets to determine the best inputs for training forecasting models. The expected fault-free behavior of multiple target variates, selected using domain knowledge, is forecasted using incoming data. The prediction errors generated from the forecasting phase are used as evidences in the DBN inference to estimate future fault probabilities. Gradual faults simulated in the virtual testbed are used to evaluate the prognosis framework. Results show that the developed framework is effective in prognosing gradual faults by leveraging the trending growth on the prediction errors. The research presented in this thesis contributes to the overall objective of developing a robust and cost-effective DBN-based framework for fault diagnosis and prognosis of building HVAC systems. Potential solutions to other existing challenges of implementing data-driven FDDP strategies, such as obtaining high-quality datasets, handling and repairing missing data, establishing a baseline model for detecting abnormalities despite other disturbances such as weather and internal conditions changes, and extracting temporal features from timeseries data are also examined.

How to extract useful knowledge from a high-dimensional and sparse (HiDS) matrix efficiently is critical for many big data-related applications. A latent factor (LF) model has been widely adopted to address this problem. It commonly relies on an iterative learning algorithm like stochastic gradient descent. However, an algorithm of this kind commonly consumes many iterations to converge, resulting in considerable time cost on large-scale datasets. How to accelerate an LF model's training process without accuracy loss becomes a vital issue. To address it, this study innovatively proposes a <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</u> ultilayered-and-randomized <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</u> atent <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</u> actor (MLF) model. Its main idea is two-fold: a) adopting randomized-learning to train LFs for implementing a ‘one-iteration’ training process for saving time; and 2) adopting the principle of a generally multilayered structure as in a deep forest or multilayered extreme learning machine to structure its LFs, thereby enhancing its representative learning ability. Empirical studies on six HiDS matrices from real applications demonstrate that compared with state-of-the-art LF models, an MLF model achieves significantly higher computational efficiency with satisfactory prediction accuracy. It has the potential to handle LF analysis on a large scale HiDS matrix with real-time requirements.

Recommender systems are designed to identify the items that a user will like or find useful based on the user's prior preferences and activities. These systems have become ubiquitous and are an essential tool for information filtering and (e-)commerce. Over the years, collaborative filtering, which derive these recommendations by leveraging past activities of groups of users, has emerged as the most prominent approach for solving this problem. This talk will present some of our recent work towards improving the performance of collaborative filtering-based recommender systems and understanding some of their fundamental limitations and characteristics. It will start by analyzing how the ratings that users provide to a set of items relate to their ratings of the set's individual items and, using these insights, will present rating prediction approaches that utilize distant supervision. It will then discuss extensions to approaches based on sparse linear and latent factor models that postulate that users' preferences are a combination of global and local preferences, which are shown to lead to better user modeling and as such improved prediction performance. Finally, the talk will conclude by discussing what can be accurately predicted by latent factor approaches and by analyzing the estimation error of sparse linear and latent factor models and how its characteristics impacts the performance of top N recommendation algorithms.

Joint latent factors and attributes to discover interpretable preferences in recommendation

Mixture factor analysis is examined as a means of flexibly estimating nonnormally distributed continuous latent factors in the presence of both continuous and dichotomous observed variables. A simulation study compares mixture factor analysis with normal maximum likelihood (ML) latent factor modeling. Different results emerge for continuous versus dichotomous outcomes. For dichotomous outcomes, normal ML path estimates have bias that worsens as latent factor skew/kurtosis increases and does not diminish as sample size increases, whereas the mixture factor analysis model produces nearly unbiased estimators as sample sizes increase (500 and greater) and offers near nominal coverage probability. For continuous outcome variables, both methods produce factor loading estimates with minimal bias regardless of latent factor skew, but the mixture factor analysis is more efficient. The method is demonstrated using data motivated by a study on youth with cystic fibrosis examining predictors of treatment adherence. In summary, mixture factor analysis provides improvements over normal ML estimation in the presence of skewed/kurtotic latent factors, but due to variability in the estimator relating the latent factor to dichotomous outcomes and computational issues, the improvements were only fully realized, in this study, at larger sample sizes (500 and greater).

In this paper, we describe a dynamic Bayesian network or DBN based approach to both two-hand gestures and one-hand gestures. Unlike wired glove-based approaches, the success of camera-based methods depends greatly on image processing and feature extraction results. So the proposed method of DBN-based inference is preceded by fail-safe steps of motion tracking. Then a new gesture recognition model for a set of both one-hand and two-hand gestures is proposed based on the dynamic Bayesian network framework which makes it easy to represent the relationship among features and incorporate new information to the model. In an experiment with ten isolated gestures, we obtained a recognition rate upwards of 99.59% with cross validation. The proposed model is believed to have a strong potential for successful applications to other related problems such as sign languages.

Rating prediction using review texts with underlying sentiments

Hand gesture recognition based on dynamic Bayesian network framework

Latent factor models have been widely used for recommendation. Most existing latent factor models mainly utilize the rating information between users and items, although some recently extended models add some auxiliary information to learn a unified latent factor between users and items. The unified latent factor only represents the latent features of users and items from the aspect of purchase history. However, the latent features of users and items may stem from different aspects, e.g., the brand-aspect and category-aspect of items. In this paper, we propose a Neural network based Aspect-level Collaborative Filtering model (NeuACF) to exploit different aspect latent factors. Through modelling rich objects and relations in recommender system as a heterogeneous information network, NeuACF first extracts different aspect-level similarity matrices of users and items through different meta-paths and then feeds an elaborately designed deep neural network with these matrices to learn aspect-level latent factors. Finally, the aspect-level latent factors are effectively fused with an attention mechanism for the top-N recommendation. Extensive experiments on three real datasets show that NeuACF significantly outperforms both existing latent factor models and recent neural network models.

In this article we propose a generalization of the linear factor model, that combines hidden Markov chain Models (HMM) with latent factor models. The HMM generates a piece-wise constant state evolution process and the observations are produced from the state vectors by a factor analysis observation process. This new switching specification provides an alternative, compact, model to handle intra-frame correlation in financial data. Furthermore, it allows variable dimension subspaces to be explored. For maximum likelihood estimation we have proposed an iterative approach based on the Expectation-Maximisation (EM) algorithm. Extensive Monte Carlo simulations and preliminary experiments obtained with a foreign exchange rate data set show promising results, especially for segmentation and tracking tasks.

Police patrols are used ubiquitously to deter crimes in urban areas. A distinctive feature of urban crimes is that criminals react opportunistically to patrol officers assignments. Compared to strategic attackers (such as terrorists) with a well-laid out plan, opportunistic criminals are less strategic in planning attacks and more flexible in executing them. In this paper, our goal is to recommend optimal police patrolling strategy against such opportunistic criminals. We first build a game-theoretic model that captures the interaction between officers and opportunistic criminals. However, while different models of adversary behavior have been proposed, their exact form remains uncertain. Rather than simply hypothesizing a model as done in previous work, one key contribution of this paper is to learn the model from real-world criminal activity data. To that end, we represent the criminal behavior and the interaction with the patrol officers as parameters of a Dynamic Bayesian Network (DBN), enabling application of standard algorithms such as EM to learn the parameters. Our second contribution is a sequence of modifications to the DBN representation, that allows for a compact representation of the model resulting in better learning accuracy and increased speed of learning of the EM algorithm when used for the modified DBN. These modifications use marginalization approaches and exploit the structure of this problem. Finally, our third contribution is an iterative learning and planning mechanism that keeps updating the adversary model periodically. We demonstrate the efficiency of our learning algorithm by applying it to a real data set of criminal activity obtained from the police department of University of Southern California (USC) situated in Los Angeles, USA. We project a significant reduction in crime rate using our planning strategy as opposed to the actual strategy deployed by the police department. We also demonstrate the improvement in crime prevention in simulations when we use our iterative planning and learning mechanism compared to just learning once and planing. This work was done in collaboration with the police department of USC.

This work introduces a novel estimation method, called LOVE, of the entries and structure of a loading matrix $A$ in a latent factor model $X=AZ+E$, for an observable random vector $X\\in \\mathbb{R}^{p}$, with correlated unobservable factors $Z\\in \\mathbb{R}^{K}$, with $K$ unknown, and uncorrelated noise $E$. Each row of $A$ is scaled, and allowed to be sparse. In order to identify the loading matrix $A$, we require the existence of pure variables, which are components of $X$ that are associated, via $A$, with one and only one latent factor. Despite the fact that the number of factors $K$, the number of the pure variables and their location are all unknown, we only require a mild condition on the covariance matrix of $Z$, and a minimum of only two pure variables per latent factor to show that $A$ is uniquely defined, up to signed permutations. Our proofs for model identifiability are constructive, and lead to our novel estimation method of the number of factors and of the set of pure variables, from a sample of size $n$ of observations on $X$. This is the first step of our LOVE algorithm, which is optimization-free, and has low computational complexity of order $p^{2}$. The second step of LOVE is an easily implementable linear program that estimates $A$. We prove that the resulting estimator is near minimax rate optimal for $A$, with respect to the $\\|\\ \\|_{\\infty ,q}$ loss, for $q\\geq 1$, up to logarithmic factors in $p$, and that it can be minimax-rate optimal in many cases of interest.\n¶ The model structure is motivated by the problem of overlapping variable clustering, ubiquitous in data science. We define the population level clusters as groups of those components of $X$ that are associated, via the matrix $A$, with the same unobservable latent factor, and multifactor association is allowed. Clusters are respectively anchored by the pure variables, and form overlapping subgroups of the $p$-dimensional random vector $X$. The Latent model approach to OVErlapping clustering is reflected in the name of our algorithm, LOVE.\n¶ The third step of LOVE estimates the clusters from the support of the columns of the estimated $A$. We guarantee cluster recovery with zero false positive proportion, and with false negative proportion control. The practical relevance of LOVE is illustrated through the analysis of a RNA-seq data set, devoted to determining the functional annotation of genes with unknown function.

The EM algorithm is a widely used technique for finding maximum likelihood (ML) estimates when the data are not fully observed. Despite its popularity for computing ML estimates in unrestricted problems and the need for simplified computations for problems with equality and inequality restrictions, there have been few applications of the algorithm to restricted ML estimation. The EM algorithm is presented for restricted ML estimation and provides its applications to the probit model under equality and inequality restrictions using two small data sets.