Stochastic gradient descent (SGD) is almost ubiquitously used for training non-convex optimization tasks. Recently, a hypothesis proposed by Keskar et al. [2017] that large batch methods tend to converge to sharp minimizers has received increasing attention. We theoretically justify this hypothesis by providing new properties of SGD in both finite-time and asymptotic regimes. In particular, we give an explicit escaping time of SGD from a local minimum in the finite-time regime and prove that SGD tends to converge to flatter minima in the asymptotic regime (although may take exponential time to converge) regardless of the batch size. We also find that SGD with a larger ratio of learning rate to batch size tends to converge to a flat minimum faster, however, its generalization performance could be worse than the SGD with a smaller ratio of learning rate to batch size. We include numerical experiments to corroborate these theoretical findings.

State-of-the-art clustering algorithms use heuristics to partition the feature space and provide little insight into the rationale for cluster membership, limiting their interpretability. In healthcare applications, the latter poses a barrier to the adoption of these methods since medical researchers are required to provide detailed explanations of their decisions in order to gain patient trust and limit liability. We present a new unsupervised learning algorithm that leverages Mixed Integer Optimization techniques to generate interpretable tree-based clustering models. Utilizing the flexible framework of Optimal Trees [1], our method approximates the globally optimal solution leading to high quality partitions of the feature space. Our algorithm, can incorporate various internal validation metrics, naturally determines the optimal number of clusters, and is able to account for mixed numeric and categorical data. It achieves comparable or superior performance on both synthetic and real world datasets when compared to K-Means while offering significantly higher interpretability.

Word vectors are at the core of many natural language processing tasks. Recently, there has been interest in post-processing word vectors to enrich their semantic information. In this paper, we introduce a novel word vector post-processing technique based on matrix conceptors (Jaeger2014), a family of regularized identity maps. More concretely, we propose to use conceptors to suppress those latent features of word vectors having high variances. The proposed method is purely unsupervised: it does not rely on any corpus or external linguistic database. We evaluate the post-processed word vectors on a battery of intrinsic lexical evaluation tasks, showing that the proposed method consistently outperforms existing state-of-the-art alternatives. We also show that post-processed word vectors can be used for the downstream natural language processing task of dialogue state tracking, yielding improved results in different dialogue domains.

Recordings of electrical brain activity carry information about a person's cognitive health. For recording EEG signals, a very common setting is for a subject to be at rest with its eyes closed. Analysis of these recordings often involve a dimensionality reduction step in which electrodes are grouped into 10 or more regions (depending on the number of electrodes available). Then an average over each group is taken which serves as a feature in subsequent evaluation. Currently, the most prominent features used in clinical practice are based on spectral power densities. In our work we consider a simplified grouping of electrodes into two regions only. In addition to spectral features we introduce a secondary, non-redundant view on brain activity through the lens of Tsallis Entropy $S_{q=2}$. We further take EEG measurements not only in an eyes closed (ec) but also in an eyes open (eo) state. For our cohort of healthy controls (HC) and individuals suffering from Parkinson's disease (PD), the question we are asking is the following: How well can one discriminate between HC and PD within this simplified, binary grouping? This question is motivated by the commercial availability of inexpensive and easy to use portable EEG devices. If enough information is retained in this binary grouping, then such simple devices could potentially be used as personal monitoring tools, as standard screening tools by general practitioners or as digital biomarkers for easy long term monitoring during neurological studies.

Spectral density matrix estimation of multivariate time series is a classical problem in time series and signal processing. In modern neuroscience, spectral density based metrics are commonly used for analyzing functional connectivity among brain regions. In this paper, we develop a non-asymptotic theory for regularized estimation of high-dimensional spectral density matrices of Gaussian and linear processes using thresholded versions of averaged periodograms. Our theoretical analysis ensures that consistent estimation of spectral density matrix of a $p$-dimensional time series using $n$ samples is possible under high-dimensional regime $\log p / n \rightarrow 0$ as long as the true spectral density is approximately sparse. A key technical component of our analysis is a new concentration inequality of average periodogram around its expectation, which is of independent interest. Our estimation consistency results complement existing results for shrinkage based estimators of multivariate spectral density, which require no assumption on sparsity but only ensure consistent estimation in a regime $p^2/n \rightarrow 0$. In addition, our proposed thresholding based estimators perform consistent and automatic edge selection when learning coherence networks among the components of a multivariate time series. We demonstrate the advantage of our estimators using simulation studies and a real data application on functional connectivity analysis with fMRI data.

While the volume of electronic health records (EHR) data continues to grow, it remains rare for hospital systems to capture dense physiological data streams, even in the data-rich intensive care unit setting. Instead, typical EHR records consist of sparse and irregularly observed multivariate time series, which are well understood to present particularly challenging problems for machine learning methods. In this paper, we present a new deep learning architecture for addressing this problem based on the use of a semi-parametric interpolation network followed by the application of a prediction network. The interpolation network allows for information to be shared across multiple dimensions during the interpolation stage, while any standard deep learning model can be used for the prediction network. We investigate the performance of this architecture on the problems of mortality and length of stay prediction.

The ability to learn and act in novel situations is still a prerogative of animate intelligence, as current machine learning methods mostly fail when moving beyond the standard i.i.d. setting. What is the reason for this discrepancy? Most machine learning tasks are anti-causal, i.e., we infer causes (labels) from effects (observations). Typically, in supervised learning we build systems that try to directly invert causal mechanisms. Instead, in this paper we argue that strong generalization capabilities crucially hinge on searching and validating meaningful hypotheses, requiring access to a causal model. In such a framework, we want to find a cause that leads to the observed effect. Anti-causal models are used to drive this search, but a causal model is required for validation. We investigate the fundamental differences between causal and anti-causal tasks, discuss implications for topics ranging from adversarial attacks to disentangling factors of variation, and provide extensive evidence from the literature to substantiate our view. We advocate for incorporating causal models in supervised learning to shift the paradigm from inference only, to search and validation.

In lifelong learning, the learner is presented with a sequence of tasks, incrementally building a data-driven prior which may be leveraged to speed up learning of a new task. In this work, we investigate the efficiency of current lifelong approaches, in terms of sample complexity, computational and memory cost. Towards this end, we first introduce a new and a more realistic evaluation protocol, whereby learners observe each example only once and hyper-parameter selection is done on a small and disjoint set of tasks, which is not used for the actual learning experience and evaluation. Second, we introduce a new metric measuring how quickly a learner acquires a new skill. Third, we propose an improved version of GEM (Lopez-Paz & Ranzato, 2017), dubbed Averaged GEM (A-GEM), which enjoys the same or even better performance as GEM, while being almost as computationally and memory efficient as EWC (Kirkpatrick et al., 2016) and other regularization-based methods. Finally, we show that all algorithms including A-GEM can learn even more quickly if they are provided with task descriptors specifying the classification tasks under consideration. Our experiments on several standard lifelong learning benchmarks demonstrate that A-GEM has the best trade-off between accuracy and efficiency.

We raise the problem of regularizing Wasserstein means and propose several terms tailored to tackle different problems. Our formulation is based on variational transportation to distribute a sparse discrete measure into the target domain without mass splitting. The resulting sparse representation well captures the desired property of the domain while maintaining a small reconstruction error. We demonstrate the scalability and robustness of our method with examples of domain adaptation and skeleton layout.

Expectation maximization (EM) algorithm is to find maximum likelihood solution for models having latent variables. A typical example is Gaussian Mixture Model (GMM) which requires Gaussian assumption, however, natural images are highly non-Gaussian so that GMM cannot be applied to perform clustering task on pixel space. To overcome such limitation, we propose a GAN based EM learning framework that can maximize the likelihood of images and estimate the latent variables with only the constraint of L-Lipschitz continuity. We call this model GAN-EM, which is a framework for image clustering, semi-supervised classification and dimensionality reduction. In M-step, we design a novel loss function for discriminator of GAN to perform maximum likelihood estimation (MLE) on data with soft class label assignments. Specifically, a conditional generator captures data distribution for $K$ classes, and a discriminator tells whether a sample is real or fake for each class. Since our model is unsupervised, the class label of real data is regarded as latent variable, which is estimated by an additional network (E-net) in E-step. The proposed GAN-EM achieves state-of-the-art clustering and semi-supervised classification results on MNIST, SVHN and CelebA, as well as comparable quality of generated images to other recently developed generative models.