This paper concerns dictionary learning, i.e., sparse coding, a fundamental representation learning problem. We show that a subgradient descent algorithm, with random initialization, can provably recover orthogonal dictionaries on a natural nonsmooth, nonconvex $\ell_1$ minimization formulation of the problem, under mild statistical assumptions on the data. This is in contrast to previous provable methods that require either expensive computation or delicate initialization schemes. Our analysis develops several tools for characterizing landscapes of nonsmooth functions, which might be of independent interest for provable training of deep networks with nonsmooth activations (e.g., ReLU), among numerous other applications. Preliminary experiments corroborate our analysis and show that our algorithm works well empirically in recovering orthogonal dictionaries.

The extraction of clusters from a dataset which includes multiple clusters and another significant portion of "background" samples is a task of practical importance. The traditional spectral clustering algorithm, relying on the leading $K$ eigenvectors to detect the $K$ clusters, fails in such cases. This paper proposes the spectral embedding norm which sums the squared values of the first $I$ (normalized) eigenvectors, where $I$ can be larger than $K$. We prove that the quantity can be used to separate clusters from the background under generic conditions motivated by applications such as anomaly detection. The performance of the algorithm is not sensitive to the choice of $I$, and we present experiments on synthetic and real-world datasets.

There has been extensive research on developing stochastic variance reduced methods to solve large-scale optimization problems. More recently, a novel algorithm of such a type named SPIDER has been developed in \cite{Fang2018}, which was shown to outperform existing algorithms of the same type and meet the lower bound in certain regimes. Though interesting in theory, SPIDER requires $\epsilon$-level stepsize to guarantee the convergence, and consequently runs slow in practice. This paper proposes SpiderBoost as an improved SPIDER scheme, which comes with two major advantages compared to SPIDER. First, it allows much larger stepsize without sacrificing the convergence rate, and hence runs substantially faster than SPIDER in practice. Second, it extends much more easily to proximal algorithms with guaranteed convergence for solving composite optimization problems, which appears challenging for SPIDER due to stringent requirement on per-iteration increment to guarantee its convergence. Both advantages can be attributed to the new convergence analysis we develop for SpiderBoost that allows much more flexibility for choosing algorithm parameters. As further generalization of SpiderBoost, we show that proximal SpiderBoost achieves a stochastic first-order oracle (SFO) complexity of $\mathcal{O}(\min\{n^{1/2}\epsilon^{-1},\epsilon^{-3/2}\})$ for composite optimization, which improves the existing best results by a factor of $\mathcal{O}(\min\{n^{1/6},\epsilon^{-1/6}\})$.

A generalized gamification framework is introduced as a form of smart infrastructure with potential to improve sustainability and energy efficiency by leveraging humans-in-the-loop strategy. The proposed framework enables a Human-Centric Cyber-Physical System using an interface to allow building managers to interact with occupants. The interface is designed for occupant engagement-integration supporting learning of their preferences over resources in addition to understanding how preferences change as a function of external stimuli such as physical control, time or incentives. Towards intelligent and autonomous incentive design, a noble statistical learning algorithm performing occupants energy usage behavior segmentation is proposed. We apply the proposed algorithm, Graphical Lasso, on energy resource usage data by the occupants to obtain feature correlations--dependencies. Segmentation analysis results in characteristic clusters demonstrating different energy usage behaviors. The features--factors characterizing human decision-making are made explainable.

We study the problem of black-box optimization of a noisy function in the presence of low-cost approximations or fidelities, which is motivated by problems like hyper-parameter tuning. In hyper-parameter tuning evaluating the black-box function at a point involves training a learning algorithm on a large data-set at a particular hyper-parameter and evaluating the validation error. Even a single such evaluation can be prohibitively expensive. Therefore, it is beneficial to use low-cost approximations, like training the learning algorithm on a sub-sampled version of the whole data-set. These low-cost approximations/fidelities can however provide a biased and noisy estimate of the function value. In this work, we incorporate the multi-fidelity setup in the powerful framework of noisy black-box optimization through tree-like hierarchical partitions. We propose a multi-fidelity bandit based tree-search algorithm for the problem and provide simple regret bounds for our algorithm. Finally, we validate the performance of our algorithm on real and synthetic datasets, where it outperforms several benchmarks.

Imbalanced Learning is an important learning algorithm for the classification models, which have enjoyed much popularity on many applications. Typically, imbalanced learning algorithms can be partitioned into two types, i.e., data level approaches and algorithm level approaches. In this paper, the focus is to develop a robust synthetic minority oversampling technique which falls the umbrella of data level approaches. On one hand, we proposed a method to generate synthetic samples in a high dimensional feature space, instead of a linear sampling space. On the other hand, in the proposed imbalanced learning framework, Gaussian Mixture Model is employed to distinguish the outliers from minority class instances and filter out the synthetic majority class instances. Last and more importantly, an adaptive optimization method is proposed to optimize these parameters in sampling process. By doing so, an effectiveness and efficiency imbalanced learning framework is developed.

ABSTRACT Learning with Label Proportions (LLP) is the problem of recovering the underlying true labels given a dataset when the data is presented in the form of bags. This paradigm is particularly suitable in contexts where providing individual labels is expensive and label aggregates are more easily obtained. In the healthcare domain, it is a burden for a patient to keep a detailed diary of their daily routines, but often they will be amenable to provide higher level summaries of daily behavior. We present a novel and efficient graph-based algorithm that encourages local smoothness and exploits the global structure of the data, while preserving the'mass' of each bag. 1. INTRODUCTION The whole spectrum of learning paradigms ranging from supervised to unsupervised learning is densely packed with different settings that have limited (or no) access to the true labels. For instance, in semi-supervised learning we have access to labels only for a subset of the dataset (usually small). Additionally, we can characterize the uncertainty in the labeling process when learning from noisy and partial labels [1, 2], using noise as a proxy in the former and a subset of labels per example in the later. Differently, in this paper we focus on learning from aggregated labels, also commonly referred to as Learning with Label Proportions (LLP) [3, 4]. In this setting, we assume the data comes in the form of bags of examples and for each of which we are given proportion of labels corresponding to each class.

In a data set comprising hundreds to thousands of neuronal time series (Brown et al., 2004), the ability to automatically identify subgroups of time series that respond similarly to an exogenous stimulus or contingency can provide insights into how neural computation is implemented at the level of groups of neurons. We consider the problem of clustering multiple time series that exhibit nonlinear dynamics into an a-priori-unknown number of subgroups. Existing model-based approaches for clustering multiple time series rely on a generative model of the time series that is a mixture of linear-Gaussian state-space models, and can be further classified according to whether the number of mixture components is assumed to be known a priori, and according to the choice of inference procedure (MCMC or variational Bayes) (Inoue et al., 2006; Chiappa and Barber, 2007; Nieto-Barajas et al., 2014; Middleton, 2014; Saad and Mansinghka, 2018). In all cases, the linear-Gaussian assumption is crucial: it enables exact evaluation of the likelihood using a Kalman filter and the ability to sample exactly from the state sequences underlying each of the time series. For nonlinear and/or non-Gaussian state-space models, this likelihood cannot be evaluated in closed form and exact sampling is not possible.

We propose an unsupervised object matching method for relational data, which finds matchings between objects in different relational datasets without correspondence information. For example, the proposed method matches documents in different languages in multi-lingual document-word networks without dictionaries nor alignment information. The proposed method assumes that each object has latent vectors, and the probability of neighbor objects is modeled by the inner-product of the latent vectors, where the neighbors are generated by short random walks over the relations. The latent vectors are estimated by maximizing the likelihood of the neighbors for each dataset. The estimated latent vectors contain hidden structural information of each object in the given relational dataset. Then, the proposed method linearly projects the latent vectors for all the datasets onto a common latent space shared across all datasets by matching the distributions while preserving the structural information. The projection matrix is estimated by minimizing the distance between the latent vector distributions with an orthogonality regularizer. To represent the distributions effectively, we use the kernel embedding of distributions that hold high-order moment information about a distribution as an element in a reproducing kernel Hilbert space, which enables us to calculate the distance between the distributions without density estimation. The structural information encoded in the latent vectors are preserved by using the orthogonality regularizer. We demonstrate the effectiveness of the proposed method with experiments using real-world multi-lingual document-word relational datasets and multiple user-item relational datasets.

Machine learning is an important tool for decision making, but its ethical and responsible application requires rigorous vetting of its interpretability and utility: an understudied problem, particularly for natural language processing models. We design a task-specific evaluation for a question answering task and evaluate how well a model interpretation improves human performance in a human-machine cooperative setting. We evaluate interpretation methods in a grounded, realistic setting: playing a trivia game as a team. We also provide design guidance for natural language processing human-in-the-loop settings.