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Music Structure Analysis (MSA) consists in segmenting a music piece in several distinct sections. We approach MSA within a compression framework, under the hypothesis that the structure is more easily revealed by a simplified representation of the original content of the song. More specifically, under the hypothesis that MSA is correlated with similarities occurring at the bar scale, linear and non-linear compression schemes can be applied to barwise audio signals. Compressed representations capture the most salient components of the different bars in the song and are then used to infer the song structure using a dynamic programming algorithm. This work explores both low-rank approximation models such as Principal Component Analysis or Nonnegative Matrix Factorization and "piece-specific" Auto-Encoding Neural Networks, with the objective to learn latent representations specific to a given song. Such approaches do not rely on supervision nor annotations, which are well-known to be tedious to collect and possibly ambiguous in MSA description. In our experiments, several unsupervised compression schemes achieve a level of performance comparable to that of state-of-the-art supervised methods (for 3s tolerance) on the RWC-Pop dataset, showcasing the importance of the barwise compression processing for MSA.

Rapid technological advances have allowed for molecular profiling across multiple omics domains from a single sample for clinical decision making in many diseases, especially cancer. As tumor development and progression are dynamic biological processes involving composite genomic aberrations, key challenges are to effectively assimilate information from these domains to identify genomic signatures and biological entities that are druggable, develop accurate risk prediction profiles for future patients, and identify novel patient subgroups for tailored therapy and monitoring. We propose integrative probabilistic frameworks for high-dimensional multiple-domain cancer data that coherently incorporate dependence within and between domains to accurately detect tumor subtypes, thus providing a catalogue of genomic aberrations associated with cancer taxonomy. We propose an innovative, flexible and scalable Bayesian nonparametric framework for simultaneous clustering of both tumor samples and genomic probes. We describe an efficient variable selection procedure to identify relevant genomic aberrations that can potentially reveal underlying drivers of a disease. Although the work is motivated by several investigations related to lung cancer, the proposed methods are broadly applicable in a variety of contexts involving high-dimensional data. The success of the methodology is demonstrated using artificial data and lung cancer omics profiles publicly available from The Cancer Genome Atlas.

Establishing a low-dimensional representation of the data leads to efficient data learning strategies. In many cases, the reduced dimension needs to be explicitly stated and estimated from the data. We explore the estimation of dimension in finite samples as a constrained optimization problem, where the estimated dimension is a maximizer of a penalized profile likelihood criterion within the framework of a probabilistic principal components analysis. Unlike other penalized maximization problems that require an "optimal" penalty tuning parameter, we propose a data-averaging procedure whereby the estimated dimension emerges as the most favourable choice over a range of plausible penalty parameters. The proposed heuristic is compared to a large number of alternative criteria in simulations and an application to gene expression data. Extensive simulation studies reveal that none of the methods uniformly dominate the other and highlight the importance of subject-specific knowledge in choosing statistical methods for dimension learning. Our application results also suggest that gene expression data have a higher intrinsic dimension than previously thought. Overall, our proposed heuristic strikes a good balance and is the method of choice when model assumptions deviated moderately.

Entity resolution (ER), comprising record linkage and de-duplication, is the process of merging noisy databases in the absence of unique identifiers to remove duplicate entities. One major challenge of analysis with linked data is identifying a representative record among determined matches to pass to an inferential or predictive task, referred to as the \emph{downstream task}. Additionally, incorporating uncertainty from ER in the downstream task is critical to ensure proper inference. To bridge the gap between ER and the downstream task in an analysis pipeline, we propose five methods to choose a representative (or canonical) record from linked data, referred to as canonicalization. Our methods are scalable in the number of records, appropriate in general data scenarios, and provide natural error propagation via a Bayesian canonicalization stage. The proposed methodology is evaluated on three simulated data sets and one application -- determining the relationship between demographic information and party affiliation in voter registration data from the North Carolina State Board of Elections. We first perform Bayesian ER and evaluate our proposed methods for canonicalization before considering the downstream tasks of linear and logistic regression. Bayesian canonicalization methods are empirically shown to improve downstream inference in both settings through prediction and coverage.

In this paper, we revisit the problem of clustering 1318 new variable stars found in the Milky way. Our recent work distinguishes these stars based on their light curves which are univariate series of brightness from the stars observed at discrete time points. This work proposes a new approach to look at these discrete series as continuous curves over time by transforming them into functional data. Then, functional principal component analysis is performed using these functional light curves. Clustering based on the significant functional principal components reveals two distinct groups of eclipsing binaries with consistency and superiority compared to our previous results. This method is established as a new powerful light curve-based classifier, where implementation of a simple clustering algorithm is effective enough to uncover the true clusters based merely on the first few relevant functional principal components. Simultaneously we discard the noise from the data study involving the higher order functional principal components. Thus the suggested method is very useful for clustering big light curve data sets which is also verified by our simulation study.

Contextualized representations based on neural language models have furthered the state of the art in various NLP tasks. Despite its great success, the nature of such representations remains a mystery. In this paper, we present an empirical property of these representations -- "average" approximates "first principal component". Specifically, experiments show that the average of these representations shares almost the same direction as the first principal component of the matrix whose columns are these representations. We believe this explains why the average representation is always a simple yet strong baseline. Our further examinations show that this property also holds in more challenging scenarios, for example, when the representations are from a model right after its random initialization. Therefore, we conjecture that this property is intrinsic to the distribution of representations and not necessarily related to the input structure. We realize that these representations empirically follow a normal distribution for each dimension, and by assuming this is true, we demonstrate that the empirical property can be in fact derived mathematically.

Graph convolution is the core of most Graph Neural Networks (GNNs) and usually approximated by message passing between direct (one-hop) neighbors. In this work, we remove the restriction of using only the direct neighbors by introducing a powerful, yet spatially localized graph convolution: Graph diffusion convolution (GDC). GDC leverages generalized graph diffusion, examples of which are the heat kernel and personalized PageRank. It alleviates the problem of noisy and often arbitrarily defined edges in real graphs. We show that GDC is closely related to spectral-based models and thus combines the strengths of both spatial (message passing) and spectral methods. We demonstrate that replacing message passing with graph diffusion convolution consistently leads to significant performance improvements across a wide range of models on both supervised and unsupervised tasks and a variety of datasets. Furthermore, GDC is not limited to GNNs but can trivially be combined with any graph-based model or algorithm (e.g. spectral clustering) without requiring any changes to the latter or affecting its computational complexity. Our implementation is available online.

This paper addresses the problem of formally verifying desirable properties of neural networks, i.e., obtaining provable guarantees that neural networks satisfy specifications relating their inputs and outputs (robustness to bounded norm adversarial perturbations, for example). Most previous work on this topic was limited in its applicability by the size of the network, network architecture and the complexity of properties to be verified. In contrast, our framework applies to a general class of activation functions and specifications on neural network inputs and outputs. We formulate verification as an optimization problem (seeking to find the largest violation of the specification) and solve a Lagrangian relaxation of the optimization problem to obtain an upper bound on the worst case violation of the specification being verified. Our approach is anytime i.e. it can be stopped at any time and a valid bound on the maximum violation can be obtained. We develop specialized verification algorithms with provable tightness guarantees under special assumptions and demonstrate the practical significance of our general verification approach on a variety of verification tasks.

Deep reinforcement learning has recently shown many impressive successes. However, one major obstacle towards applying such methods to real-world problems is their lack of data-efficiency. To this end, we propose the Bottleneck Simulator: a model-based reinforcement learning method which combines a learned, factorized transition model of the environment with rollout simulations to learn an effective policy from few examples. The learned transition model employs an abstract, discrete (bottleneck) state, which increases sample efficiency by reducing the number of model parameters and by exploiting structural properties of the environment. We provide a mathematical analysis of the Bottleneck Simulator in terms of fixed points of the learned policy, which reveals how performance is affected by four distinct sources of error: an error related to the abstract space structure, an error related to the transition model estimation variance, an error related to the transition model estimation bias, and an error related to the transition model class bias. Finally, we evaluate the Bottleneck Simulator on two natural language processing tasks: a text adventure game and a real-world, complex dialogue response selection task. On both tasks, the Bottleneck Simulator yields excellent performance beating competing approaches.

Modern communication networks have become very complicated and highly dynamic, which makes them hard to model, predict and control. In this paper, we develop a novel experience-driven approach that can learn to well control a communication network from its own experience rather than an accurate mathematical model, just as a human learns a new skill (such as driving, swimming, etc). Specifically, we, for the first time, propose to leverage emerging Deep Reinforcement Learning (DRL) for enabling model-free control in communication networks; and present a novel and highly effective DRL-based control framework, DRL-TE, for a fundamental networking problem: Traffic Engineering (TE). The proposed framework maximizes a widely-used utility function by jointly learning network environment and its dynamics, and making decisions under the guidance of powerful Deep Neural Networks (DNNs). We propose two new techniques, TE-aware exploration and actor-critic-based prioritized experience replay, to optimize the general DRL framework particularly for TE. To validate and evaluate the proposed framework, we implemented it in ns-3, and tested it comprehensively with both representative and randomly generated network topologies. Extensive packet-level simulation results show that 1) compared to several widely-used baseline methods, DRL-TE significantly reduces end-to-end delay and consistently improves the network utility, while offering better or comparable throughput; 2) DRL-TE is robust to network changes; and 3) DRL-TE consistently outperforms a state-ofthe-art DRL method (for continuous control), Deep Deterministic Policy Gradient (DDPG), which, however, does not offer satisfying performance.