Learning accurate prior knowledge of natural images is of great importance for single image super-resolution (SR). Existing SR methods either learn the prior from the low/high-resolution patch pairs or estimate the prior models from the input low-resolution (LR) image. Specifically, high-frequency details are learned in the former methods. Though effective, they are heuristic and have limitations in dealing with blurred LR images; while the latter suffers from the limitations of frequency aliasing. In this paper, we propose to combine those two lines of ideas for image super-resolution. More specifically, the parametric sparse prior of the desirable high-resolution (HR) image patches are learned from both the input low-resolution (LR) image and a training image dataset. With the learned sparse priors, the sparse codes and thus the HR image patches can be accurately recovered by solving a sparse coding problem. Experimental results show that the proposed SR method outperforms existing state-of-the-art methods in terms of both subjective and objective image qualities.

We consider the weakly supervised binary classification problem where the labels are randomly flipped with probability $1-\alpha$. Although there exist numerous algorithms for this problem, it remains theoretically unexplored how the statistical accuracies and computational efficiency of these algorithms depend on the degree of supervision, which is quantified by $\alpha$. In this paper, we characterize the effect of $\alpha$ by establishing the information-theoretic and computational boundaries, namely, the minimax-optimal statistical accuracy that can be achieved by all algorithms, and polynomial-time algorithms under an oracle computational model. For small $\alpha$, our result shows a gap between these two boundaries, which represents the computational price of achieving the information-theoretic boundary due to the lack of supervision. Interestingly, we also show that this gap narrows as $\alpha$ increases. In other words, having more supervision, i.e., more correct labels, not only improves the optimal statistical accuracy as expected, but also enhances the computational efficiency for achieving such accuracy.

We develop a scalable, computationally efficient method for the task of energy disaggregation for home appliance monitoring. In this problem the goal is to estimate the energy consumption of each appliance based on the total energy-consumption signal of a household. The current state of the art models the problem as inference in factorial HMMs, and finds an approximate solution to the resulting quadratic integer program via quadratic programming. Here we take a more principled approach, better suited to integer programming problems, and find an approximate optimum by combining convex semidefinite relaxations with randomized rounding, as well as with a scalable ADMM method that exploits the special structure of the resulting semidefinite program. Simulation results demonstrate the superiority of our methods both in synthetic and real-world datasets.

Estimators of information theoretic measures such as entropy and mutual information from samples are a basic workhorse for many downstream applications in modern data science. State of the art approaches have been either geometric (nearest neighbor (NN) based) or kernel based (with bandwidth chosen to be data independent and vanishing sub linearly in the sample size). In this paper we combine both these approaches to design new estimators of entropy and mutual information that strongly outperform all state of the art methods. Our estimator uses bandwidth choice of fixed $k$-NN distances; such a choice is both data dependent and linearly vanishing in the sample size and necessitates a bias cancellation term that is universal and independent of the underlying distribution. As a byproduct, we obtain a unified way of obtaining both kernel and NN estimators. The corresponding theoretical contribution relating the geometry of NN distances to asymptotic order statistics is of independent mathematical interest.

We provide two fundamental results on the population (infinite-sample) likelihood function of Gaussian mixture models with $M \geq 3$ components. Our first main result shows that the population likelihood function has bad local maxima even in the special case of equally-weighted mixtures of well-separated and spherical Gaussians. We prove that the log-likelihood value of these bad local maxima can be arbitrarily worse than that of any global optimum, thereby resolving an open question of Srebro (2007). Our second main result shows that the EM algorithm (or a first-order variant of it) with random initialization will converge to bad critical points with probability at least $1-e^{-\Omega(M)}$. We further establish that a first-order variant of EM will not converge to strict saddle points almost surely, indicating that the poor performance of the first-order method can be attributed to the existence of bad local maxima rather than bad saddle points. Overall, our results highlight the necessity of careful initialization when using the EM algorithm in practice, even when applied in highly favorable settings.

Reasoning about objects, relations, and physics is central to human intelligence, and a key goal of artificial intelligence. Here we introduce the interaction network, a model which can reason about how objects in complex systems interact, supporting dynamical predictions, as well as inferences about the abstract properties of the system. Our model takes graphs as input, performs object-and relation-centric reasoning in a way that is analogous to a simulation, and is implemented using deep neural networks. We evaluate its ability to reason about several challenging physical domains: n-body problems, rigid-body collision, and non-rigid dynamics. Our results show it can be trained to accurately simulate the physical trajectories of dozens of objects over thousands of time steps, estimate abstract quantities such as energy, and generalize automatically to systems with different numbers and configurations of objects and relations. Our interaction network implementation is the first general-purpose, learnable physics engine, and a powerful general framework for reasoning about object and relations in a wide variety of complex real-world domains.

We present a theoretical analysis of active learning with more realistic interactions with human oracles. Previous empirical studies have shown oracles abstaining on difficult queries until accumulating enough information to make label decisions. We formalize this phenomenon with an "oracle epiphany model" and analyze active learning query complexity under such oracles for both the realizable and the agnostic cases. Our analysis shows that active learning is possible with oracle epiphany, but incurs an additional cost depending on when the epiphany happens. Our results suggest new, principled active learning approaches with realistic oracles.

Accuracy and interpretability are two dominant features of successful predictive models. Typically, a choice must be made in favor of complex black box models such as recurrent neural networks (RNN) for accuracy versus less accurate but more interpretable traditional models such as logistic regression. This tradeoff poses challenges in medicine where both accuracy and interpretability are important. We addressed this challenge by developing the REverse Time AttentIoN model (RETAIN) for application to Electronic Health Records (EHR) data. RETAIN achieves high accuracy while remaining clinically interpretable and is based on a two-level neural attention model that detects influential past visits and significant clinical variables within those visits (e.g.

A fundamental problem in cognitive neuroscience is how humans make decisions, act, and behave in relation to other humans. Here we adopt the hypothesis that when we are in an interactive social setting, our brains perform Bayesian inference of the intentions and cooperativeness of others using probabilistic representations. We employ the framework of partially observable Markov decision processes (POMDPs) to model human decision making in a social context, focusing specifically on the volunteer's dilemma in a version of the classic Public Goods Game. We show that the POMDP model explains both the behavior of subjects as well as neural activity recorded using fMRI during the game. The decisions of subjects can be modeled across all trials using two interpretable parameters. Furthermore, the expected reward predicted by the model for each subject was correlated with the activation of brain areas related to reward expectation in social interactions. Our results suggest a probabilistic basis for human social decision making within the framework of expected reward maximization.

In this paper, we propose a very deep fully convolutional encoding-decoding framework for image restoration such as denoising and super-resolution. The network is composed of multiple layers of convolution and deconvolution operators, learning end-to-end mappings from corrupted images to the original ones. The convolutional layers act as the feature extractor, which capture the abstraction of image contents while eliminating noises/corruptions. Deconvolutional layers are then used to recover the image details. We propose to symmetrically link convolutional and deconvolutional layers with skip-layer connections, with which the training converges much faster and attains a higher-quality local optimum. First, the skip connections allow the signal to be back-propagated to bottom layers directly, and thus tackles the problem of gradient vanishing, making training deep networks easier and achieving restoration performance gains consequently. Second, these skip connections pass image details from convolutional layers to deconvolutional layers, which is beneficial in recovering the original image. Significantly, with the large capacity, we can handle different levels of noises using a single model. Experimental results show that our network achieves better performance than recent state-of-the-art methods.