Time-invariant linear dynamical system arises in many real-world applications,and its usefulness is widely acknowledged. A practical limitation with this model is that its latent dimension that has a large impact on the model capability needs to be manually specified. It can be demonstrated that a lower-order model class could be totally nested into a higher-order class, and the corresponding likelihood is nondecreasing. Hence, criterion built on the likelihood is not appropriate for model selection. This paper addresses the issue and proposes a criterion for linear dynamical system based on the principle of minimum description length. The latent structure, which is omitted in previous work, is explicitly considered in this newly proposed criterion. Our work extends the principle of minimum description length and demonstrates its effectiveness in the tasks of model training. The experiments on both univariate and multivariate sequences confirm the good performance of our newly proposed method.

We propose a novel family of band-pass filters for efficient spectral decomposition of signals. Previous work has already established the effectiveness of representations based on static band-pass filtering of speech signals (e.g., mel-frequency cepstral coefficients and deep scattering spectrum). A potential shortcoming of these approaches is the fact that the parameters specifying such a representation are fixed a priori and not learned using the available data. To address this limitation, we propose a family of filters defined via cosine modulations of Parzen windows, where the modulation frequency models the center of a spectral band-pass filter and the length of a Parzen window is inversely proportional to the filter width in the spectral domain. We propose to learn such a representation using stochastic variational Bayesian inference based on Gaussian dropout posteriors and sparsity inducing priors. Such a prior leads to an intractable integral defining the Kullback--Leibler divergence term for which we propose an effective approximation based on the Gauss--Hermite quadrature. Our empirical results demonstrate that the proposed approach is competitive with state-of-the-art models on speech recognition tasks.

Bayesian optimization offers a flexible framework to optimize an objective function that is expensive to be evaluated. A Bayesian optimizer iteratively queries the function values on its carefully selected points. Subsequently, it makes a sensible recommendation about where the optimum locates based on its accumulated knowledge. This procedure usually demands a long execution time. In practice, however, there often exists a computational budget or an evaluation limitation allocated to an optimizer, due to the resource scarcity. This constraint demands an optimizer to be aware of its remaining budget and able to spend it wisely, in order to return as better a point as possible. In this paper, we propose a Bayesian optimization approach in this evaluation-limited scenario. Our approach is based on constraining searching directions so as to dedicate the model capability to the most promising area. It could be viewed as a combination of local and global searching policies, which aims at reducing inefficient exploration in the local searching areas, thus making a searching policy more efficient. Experimental studies are conducted on both synthetic and real-world applications. The results demonstrate the superior performance of our newly proposed approach in searching for the optimum within a prescribed evaluation budget.

The interpretability of machine learning, particularly for deep neural networks, is strongly required when performing decision-making in a real-world application. There are several studies that show that interpretability is obtained by replacing a non-explainable neural network with an explainable simplified surrogate model. Meanwhile, another approach to understanding the target system is simulation modeled by human knowledge with interpretable simulation parameters. Recently developed simulation learning based on applications of kernel mean embedding is a method used to estimate simulation parameters as posterior distributions. However, there was no relation between the machine learning model and the simulation model. Furthermore, the computational cost of simulation learning is very expensive because of the complexity of the simulation model. To address these difficulties, we propose a ``model bridging'' framework to bridge machine learning models with simulation models by a series of kernel mean embeddings. The proposed framework enables us to obtain predictions and interpretable simulation parameters simultaneously without the computationally expensive calculations associated with simulations. In this study, we investigate a Bayesian neural network model with a few hidden layers serving as an un-explainable machine learning model. We apply the proposed framework to production simulation, which is important in the manufacturing industry.

We implement gradient-based variational inference routines for Wishart and inverse Wishart processes, which we apply as Bayesian models for the dynamic, heteroskedastic covariance matrix of a multivariate time series. The Wishart and inverse Wishart processes are constructed from i.i.d. Gaussian processes, for which we apply existing black-box variational inference algorithms for approximate Gaussian process inference. These methods scale well with the length of the time series, however, they fail in the case of the Wishart process, an issue we resolve with a simple modification into an additive white noise parameterization of the model. This modification is also key to implementing a factored variant of the construction, allowing inference to additionally scale to high-dimensional covariance matrices. As with existing MCMC-based inference routines for the Wishart and inverse Wishart processes, we show that these variational alternatives significantly outperform multivariate GARCH baselines when forecasting the covariances of returns on financial instruments.

Ensemble learning, the machine learning paradigm where multiple algorithms are combined, has exhibited promising perfomance in a variety of tasks. The present work focuses on unsupervised ensemble classification. The term unsupervised refers to the ensemble combiner who has no knowledge of the ground-truth labels that each classifier has been trained on. While most prior works on unsupervised ensemble classification are designed for independent and identically distributed (i.i.d.) data, the present work introduces an unsupervised scheme for learning from ensembles of classifiers in the presence of data dependencies. Two types of data dependencies are considered: sequential data and networked data whose dependencies are captured by a graph. Moment matching and Expectation Maximization algorithms are developed for the aforementioned cases, and their performance is evaluated on synthetic and real datasets.

This dissertation proposes efficient algorithms and provides theoretical analysis through the angle of spectral methods for some important non-convex optimization problems in machine learning. Specifically, the focus is on two types of non-convex optimization problems: learning the parameters of latent variable models and learning in deep neural networks. Learning latent variable models is traditionally framed as a non-convex optimization problem through Maximum Likelihood Estimation (MLE). For some specific models such as multi-view model, it's possible to bypass the non-convexity by leveraging the special model structure and convert the problem into spectral decomposition through Methods of Moments (MM) estimator. In this research, a novel algorithm is proposed that can flexibly learn a multi-view model in a non-parametric fashion.

One of the primary goals of AI research is the development of artificial agents that can exceed human performance on a wide range of cognitive tasks, in other words, artificial general intelligence (AGI). Although the development of AGI has many potential benefits, there are also many safety concerns that have been raised in the literature [Bostrom, 2014; Everitt et al., 2018; Amodei et al., 2016]. Various approaches for addressing AGI safety have been proposed [Leike et al., 2018; Christiano et al., 2018; Irving et al., 2018; Hadfield-Menell et al., 2016; Everitt, 2018], often presented as a modification of the reinforcement learning (RL) framework, or a new framework altogether. Understanding and comparing different frameworks for AGI safety can be difficult because they build on differing concepts and assumptions. For example, both reward modeling [Leike et al., 2018] and cooperative inverse RL [Hadfield-Menell et al., 2016] are frameworks for making an agent learn the preferences of a human user, but what are the key differences between them?

In this paper we offer a preliminary study of the application of Bayesian coresets to network security data. Network intrusion detection is a field that could take advantage of Bayesian machine learning in modelling uncertainty and managing streaming data; however, the large size of the data sets often hinders the use of Bayesian learning methods based on MCMC. Limiting the amount of useful data is a central problem in a field like network traffic analysis, where large amount of redundant data can be generated very quickly via packet collection. Reducing the number of samples would not only make learning more feasible, but would also contribute to reduce the need for memory and storage. We explore here the use of Bayesian coresets, a technique that reduces the amount of data samples while guaranteeing the learning of an accurate posterior distribution using Bayesian learning. We analyze how Bayesian coresets affect the accuracy of learned models, and how time-space requirements are traded-off, both in a static scenario and in a streaming scenario.

The accuracy of an integral approximation via Monte Carlo sampling depends on the distribution of the integrand and the existence of its moments. In importance sampling, the choice of the proposal distribution markedly affects the existence of these moments and thus the accuracy of the obtained integral approximation. In this work, we present a method for improving the proposal distribution that applies to complicated distributions which are not available in closed form. The method iteratively matches the moments of a sample from the proposal distribution to their importance weighted moments, and is applicable to both standard importance sampling and self-normalized importance sampling. We apply the method to Bayesian leave-one-out cross-validation and show that it can significantly improve the accuracy of model assessment compared to regular Monte Carlo sampling or importance sampling when there are influential observations. We also propose a diagnostic method that can estimate the convergence rate of any Monte Carlo estimator from a finite random sample.