Understanding Music Semantics and User Behavior with Probabilistic Latent Variable Models

Bayesian probabilistic modeling provides a powerful framework for building flexible models to incorporate latent structures through likelihood model and prior. When we specify a model, we make certain assumptions about the underlying data-generating process with respect to these latent structures. For example, the latent Dirichlet allocation (LDA) model assumes that when generating a document, we first select a latent topic and then select a word that often appears in the selected topic. We can uncover the latent structures conditioned on the observed data via posterior inference. In this dissertation, we apply the tools of probabilistic latent variable models and try to understand complex real-world data about music semantics and user behavior. We first look into the problem of automatic music tagging -- inferring the semantic tags (e.g., "jazz'', "piano'', "happy'', etc.) from the audio features. We treat music tagging as a matrix completion problem and apply the Poisson matrix factorization model jointly on the vector-quantized audio features and a "bag-of-tags'' representation. This approach exploits the shared latent structure between semantic tags and acoustic codewords. We present experimental results on the Million Song Dataset for both annotation and retrieval tasks, illustrating the steady improvement in performance as more data is used. We then move to the intersection between music semantics and user behavior: music recommendation. The leading performance in music recommendation is achieved by collaborative filtering methods which exploit the similarity patterns in user's listening history. We address the fundamental cold-start problem of collaborative filtering: it cannot recommend new songs that no one has listened to. We train a neural network on semantic tagging information as a content model and use it as a prior in a collaborative filtering model. The proposed system is evaluated on the Million Song Dataset and shows comparably better result than the collaborative filtering approaches, in addition to the favorable performance in the cold-start case. Finally, we focus on general recommender systems. We examine two different types of data: implicit and explicit feedback, and introduce the notion of user exposure (whether or not a user is exposed to an item) as part of the data-generating process, which is latent for implicit data and observed for explicit data. For implicit data, we propose a probabilistic matrix factorization model and infer the user exposure from data. In the language of causal analysis (Imbens and Rubin, 2015), user exposure has close connection to the assignment mechanism. We leverage this connection more directly for explicit data and develop a causal inference approach to recommender systems. We demonstrate that causal inference for recommender systems leads to improved generalization to new data. Exact posterior inference is generally intractable for latent variables models. Throughout this thesis, we will design specific inference procedure to tractably analyze the large-scale data encountered under each scenario

Prior specification via prior predictive matching: Poisson matrix factorization and beyond

Hyperparameter optimization for machine learning models is typically carried out by some sort of cross-validation procedure or global optimization, both of which require running the learning algorithm numerous times. We show that for Bayesian hierarchical models there is an appealing alternative that allows selecting good hyperparameters without learning the model parameters during the process at all, facilitated by the prior predictive distribution that marginalizes out the model parameters. We propose an approach that matches suitable statistics of the prior predictive distribution with ones provided by an expert and apply the general concept for matrix factorization models. For some Poisson matrix factorization models we can analytically obtain exact hyperparameters, including the number of factors, and for more complex models we propose a model-independent optimization procedure

Composing Deep Learning and Bayesian Nonparametric Methods

Recent progress in Bayesian methods largely focus on non-conjugate models featured with extensive use of black-box functions: continuous functions implemented with neural networks. Using deep neural networks, Bayesian models can reasonably fit big data while at the same time capturing model uncertainty. This thesis targets at a more challenging problem: how do we model general random objects, including discrete ones, using random functions? Our conclusion is: many (discrete) random objects are in nature a composition of Poisson processes and random functions}. Thus, all discreteness is handled through the Poisson process while random functions captures the rest complexities of the object. Thus the title: composing deep learning and Bayesian nonparametric methods. This conclusion is not a conjecture. In spacial cases such as latent feature models , we can prove this claim by working on infinite dimensional spaces, and that is how Bayesian nonparametric kicks in. Moreover, we will assume some regularity assumptions on random objects such as exchangeability. Then the representations will show up magically using representation theorems. We will see this two times throughout this thesis. One may ask: when a random object is too simple, such as a non-negative random vector in the case of latent feature models, how can we exploit exchangeability? The answer is to aggregate infinite random objects and map them altogether onto an infinite dimensional space. And then assume exchangeability on the infinite dimensional space. We demonstrate two examples of latent feature models by (1) concatenating them as an infinite sequence (Section 2,3) and (2) stacking them as a 2d array (Section 4). Besides, we will see that Bayesian nonparametric methods are useful to model discrete patterns in time series data. We will showcase two examples: (1) using variance Gamma processes to model change points (Section 5), and (2) using Chinese restaurant processes to model speech with switching speakers (Section 6). We also aware that the inference problem can be non-trivial in popular Bayesian nonparametric models. In Section 7, we find a novel solution of online inference for the popular HDP-HMM model

COMMUNITY DETECTION IN GRAPHS

Thesis (Ph.D.) - Indiana University, Luddy School of Informatics, Computing, and Engineering/University Graduate School, 2020Community detection has always been one of the fundamental research topics in graph mining. As a type of unsupervised or semi-supervised approach, community detection aims to explore node high-order closeness by leveraging graph topological structure. By grouping similar nodes or edges into the same community while separating dissimilar ones apart into different communities, graph structure can be revealed in a coarser resolution. It can be beneficial for numerous applications such as user shopping recommendation and advertisement in e-commerce, protein-protein interaction prediction in the bioinformatics, and literature recommendation or scholar collaboration in citation analysis. However, identifying communities is an ill-defined problem. Due to the No Free Lunch theorem [1], there is neither gold standard to represent perfect community partition nor universal methods that are able to detect satisfied communities for all tasks under various types of graphs. To have a global view of this research topic, I summarize state-of-art community detection methods by categorizing them based on graph types, research tasks and methodology frameworks. As academic exploration on community detection grows rapidly in recent years, I hereby particularly focus on the state-of-art works published in the latest decade, which may leave out some classic models published decades ago. Meanwhile, three subtle community detection tasks are proposed and assessed in this dissertation as well. First, apart from general models which consider only graph structures, personalized community detection considers user need as auxiliary information to guide community detection. In the end, there will be fine-grained communities for nodes better matching user needs while coarser-resolution communities for the rest of less relevant nodes. Second, graphs always suffer from the sparse connectivity issue. Leveraging conventional models directly on such graphs may hugely distort the quality of generate communities. To tackle such a problem, cross-graph techniques are involved to propagate external graph information as a support for target graph community detection. Third, graph community structure supports a natural language processing (NLP) task to depict node intrinsic characteristics by generating node summarizations via a text generative model. The contribution of this dissertation is threefold. First, a decent amount of researches are reviewed and summarized under a well-defined taxonomy. Existing works about methods, evaluation and applications are all addressed in the literature review. Second, three novel community detection tasks are demonstrated and associated models are proposed and evaluated by comparing with state-of-art baselines under various datasets. Third, the limitations of current works are pointed out and future research tracks with potentials are discussed as well

Overlapping Communities on Large-Scale Networks: Benchmark Generation and Learning via Adaptive Stochastic Optimization

This dissertation builds on two lines of research that are related to the task of community detection on large-scale network data. Our first contribution is a novel generator for large-scale networks with overlapping communities. Synthetic generators are essential for algorithm testing and simulation studies for networks, as these data are scarce and constantly evolving. We propose a generator based on a flexible random graph model that allows for the control of two complementary measures of centrality -- the degree centrality and the eigencentrality. For an arbitrary centrality target and community structure, we study the problem of recovering the model parameters that enforce such targets in expectation. We find that this problem always admits a solution in the parameter space, which is also unique for large graphs. We propose to recover this solution via a properly initialized multivariate-Newton Raphson algorithm. The resulting benchmark generator is able to simulate networks with a billion edges and hundreds of millions of nodes in 30 seconds, while reproducing a wide spectrum of network topologies -- including assortative mixing and power-law centrality distributions. Our second contribution involves variance reduction techniques for stochastic variational inference (SVI). SVI scales approximate inference to large-scale data -- including massive networks -- via stochastic optimization. SVI is efficient because, at each iteration, it only uses a random minibatch of the data to produce a noisy estimate of the gradient. However, such estimates can suffer from high variance, which slows down convergence. One strategy to reduce the variance of the gradient is to use importance sampling, biasing the distribution of data for each minibatch towards the data points that are most influential to the inference at hand. Here, we develop an importance sampling strategy for SVI. Our adaptive stochastic variational inference algorithm (AdaSVI) reweights the sampling distribution to minimize the variance of the stochastic natural gradient. We couple the importance sampling strategy with an adaptive learning rate providing a parameter-free stochastic optimization algorithm where the only user input required is the minibatch size. We study AdaSVI on a matrix factorization model and find that it significantly improves SVI, leading to faster convergence on synthetic data

Sequential decision making in artificial musical intelligence

Over the past 60 years, artificial intelligence has grown from a largely academic field of research to a ubiquitous array of tools and approaches used in everyday technology. Despite its many recent successes and growing prevalence, certain meaningful facets of computational intelligence have not been as thoroughly explored. Such additional facets cover a wide array of complex mental tasks which humans carry out easily, yet are difficult for computers to mimic. A prime example of a domain in which human intelligence thrives, but machine understanding is still fairly limited, is music. Over the last decade, many researchers have applied computational tools to carry out tasks such as genre identification, music summarization, music database querying, and melodic segmentation. While these are all useful algorithmic solutions, we are still a long way from constructing complete music agents, able to mimic (at least partially) the complexity with which humans approach music. One key aspect which hasn't been sufficiently studied is that of sequential decision making in musical intelligence. This thesis strives to answer the following question: Can a sequential decision making perspective guide us in the creation of better music agents, and social agents in general? And if so, how? More specifically, this thesis focuses on two aspects of musical intelligence: music recommendation and human-agent (and more generally agent-agent) interaction in the context of music. The key contributions of this thesis are the design of better music playlist recommendation algorithms; the design of algorithms for tracking user preferences over time; new approaches for modeling people's behavior in situations that involve music; and the design of agents capable of meaningful interaction with humans and other agents in a setting where music plays a roll (either directly or indirectly). Though motivated primarily by music-related tasks, and focusing largely on people's musical preferences, this thesis also establishes that insights from music-specific case studies can also be applicable in other concrete social domains, such as different types of content recommendation. Showing the generality of insights from musical data in other contexts serves as evidence for the utility of music domains as testbeds for the development of general artificial intelligence techniques. Ultimately, this thesis demonstrates the overall usefulness of taking a sequential decision making approach in settings previously unexplored from this perspectiveComputer Science