We study mechanisms to characterize how the asymptotic convergence of backpropagation in deep architectures, in general, is related to the network structure, and how it may be influenced by other design choices including activation type, denoising and dropout rate. We seek to analyze whether network architecture and input data statistics may guide the choices of learning parameters and vice versa. Given the broad applicability of deep architectures, this issue is interesting both from theoretical and a practical standpoint. Using properties of general nonconvex objectives (with first-order information), we first build the association between structural, distributional and learnability aspects of the network vis-\`a-vis their interaction with parameter convergence rates. We identify a nice relationship between feature denoising and dropout, and construct families of networks that achieve the same level of convergence. We then derive a workflow that provides systematic guidance regarding the choice of network sizes and learning parameters often mediated4 by input statistics. Our technical results are corroborated by an extensive set of evaluations, presented in this paper as well as independent empirical observations reported by other groups. We also perform experiments showing the practical implications of our framework for choosing the best fully-connected design for a given problem.

We propose a new family of optimization criteria for variational auto-encoding models, generalizing the standard evidence lower bound. We provide conditions under which they recover the data distribution and learn latent features, and formally show that common issues such as blurry samples and uninformative latent features arise when these conditions are not met. Based on these new insights, we propose a new sequential VAE model that can generate sharp samples on the LSUN image dataset based on pixel-wise reconstruction loss, and propose an optimization criterion that encourages unsupervised learning of informative latent features.

We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse plus low-rank components, we propose a sparsity constrained maximum likelihood estimator based on matrix factorization, and an efficient alternating gradient descent algorithm with hard thresholding to solve it. Our algorithm is orders of magnitude faster than the convex relaxation based methods for LVGGM. In addition, we prove that our algorithm is guaranteed to linearly converge to the unknown sparse and low-rank components up to the optimal statistical precision. Experiments on both synthetic and genomic data demonstrate the superiority of our algorithm over the state-of-the-art algorithms and corroborate our theory.

We present an approach to deep estimation of discrete conditional probability distributions. Such models have several applications, including generative modeling of audio, image, and video data. Our approach combines two main techniques: dyadic partitioning and graph-based smoothing of the discrete space. By recursively decomposing each dimension into a series of binary splits and smoothing over the resulting distribution using graph-based trend filtering, we impose a strict structure to the model and achieve much higher sample efficiency. We demonstrate the advantages of our model through a series of benchmarks on both synthetic and real-world datasets, in some cases reducing the error by nearly half in comparison to other popular methods in the literature. All of our models are implemented in Tensorflow and publicly available at https://github.com/tansey/sdp .

Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks. Despite their practical importance, graphlets have been severely limited to applications and domains with relatively small graphs. Most previous work has focused on exact algorithms, however, it is often too expensive to compute graphlets exactly in massive networks with billions of edges, and finding an approximate count is usually sufficient for many applications. In this work, we propose an unbiased graphlet estimation framework that is (a) fast with significant speedups compared to the state-of-the-art, (b) parallel with nearly linear-speedups, (c) accurate with <1% relative error, (d) scalable and space-efficient for massive networks with billions of edges, and (e) flexible for a variety of real-world settings, as well as estimating macro and micro-level graphlet statistics (e.g., counts) of both connected and disconnected graphlets. In addition, an adaptive approach is introduced that finds the smallest sample size required to obtain estimates within a given user-defined error bound. On 300 networks from 20 domains, we obtain <1% relative error for all graphlets. This is significantly more accurate than existing methods while using less data. Moreover, it takes a few seconds on billion edge graphs (as opposed to days/weeks). These are by far the largest graphlet computations to date.

Recurrent neural networks (RNNs) process input text sequentially and model the conditional transition between word tokens. In contrast, the advantages of recursive networks include that they explicitly model the compositionality and the recursive structure of natural language. However, the current recursive architecture is limited by its dependence on syntactic tree. In this paper, we introduce a robust syntactic parsing-independent tree structured model, Neural Tree Indexers (NTI) that provides a middle ground between the sequential RNNs and the syntactic treebased recursive models. NTI constructs a full n-ary tree by processing the input text with its node function in a bottom-up fashion. Attention mechanism can then be applied to both structure and node function. We implemented and evaluated a binarytree model of NTI, showing the model achieved the state-of-the-art performance on three different NLP tasks: natural language inference, answer sentence selection, and sentence classification, outperforming state-of-the-art recurrent and recursive neural networks.

Tree ensembles, such as random forests and boosted trees, are renowned for their high prediction performance. However, their interpretability is critically limited due to the enormous complexity. In this study, we present a method to make a complex tree ensemble interpretable by simplifying the model. Specifically, we formalize the simplification of tree ensembles as a model selection problem. Given a complex tree ensemble, we aim at obtaining the simplest representation that is essentially equivalent to the original one. To this end, we derive a Bayesian model selection algorithm that optimizes the simplified model while maintaining the prediction performance. Our numerical experiments on several datasets showed that complicated tree ensembles were reasonably approximated as interpretable.

In order for autonomous robots to operate in unstructured environments, several perceptual capabilities are required. Most of these skills cannot be hard-coded in the system beforehand, but need to be developed and learned over time as the agent explores and acquires novel experience. As a prototypical example of this setting, in this work we consider the task of visual object recognition in robotics: Images depicting different objects are received one frame at a time, and the system needs to incrementally update the internal model of known objects as new examples are gathered. In the last few years, machine learning has achieved remarkable results in a variety of applications for robotics and computer vision [1], [2], [3]. However, most of these methods have been developed for off-line (or "batch") settings, where the entire training set is available beforehand. The problem of updating a learned model online has been addressed in the literature [4], [5], [6], [7], but most algorithms proposed in this context do not take into account challenges that are characteristic of realistic lifelong learning applications. Specifically, in online classification settings, a major challenge is to cope with the situation in which a novel class is added to the model. Indeed, 1) most learning algorithms require the number of classes to be known beforehand and not grow indefinitely, and 2) the imbalance between the few examples of the new class (potentially just one) and the many examples of previously learned classes can lead to unexpected and undesired behaviors [8].

Hypothesis testing is an important cognitive process that supports human reasoning. In this paper, we introduce a computational hypothesis testing approach based on memory augmented neural networks. Our approach involves a hypothesis testing loop that reconsiders and progressively refines a previously formed hypothesis in order to generate new hypotheses to test. We apply the proposed approach to language comprehension task by using Neural Semantic Encoders (NSE). Our NSE models achieve the state-of-the-art results showing an absolute improvement of 1.2% to 2.6% accuracy over previous results obtained by single and ensemble systems on standard machine comprehension benchmarks such as the Children's Book Test (CBT) and Who-Did-What (WDW) news article datasets.

While great strides have been made in using deep learning algorithms to solve supervised learning tasks, the problem of unsupervised learning - leveraging unlabeled examples to learn about the structure of a domain - remains a difficult unsolved challenge. Here, we explore prediction of future frames in a video sequence as an unsupervised learning rule for learning about the structure of the visual world. We describe a predictive neural network ("PredNet") architecture that is inspired by the concept of "predictive coding" from the neuroscience literature. These networks learn to predict future frames in a video sequence, with each layer in the network making local predictions and only forwarding deviations from those predictions to subsequent network layers. We show that these networks are able to robustly learn to predict the movement of synthetic (rendered) objects, and that in doing so, the networks learn internal representations that are useful for decoding latent object parameters (e.g. pose) that support object recognition with fewer training views. We also show that these networks can scale to complex natural image streams (car-mounted camera videos), capturing key aspects of both egocentric movement and the movement of objects in the visual scene, and the representation learned in this setting is useful for estimating the steering angle. Altogether, these results suggest that prediction represents a powerful framework for unsupervised learning, allowing for implicit learning of object and scene structure.