Unsupervised learning of structured predictors has been a long standing pursuit in machine learning. Recently a conditional random field auto-encoder has been proposed in a two-layer setting, allowing latent structured representation to be automatically inferred. Aside from being nonconvex, it also requires the demanding inference of normalization. In this paper, we develop a convex relaxation of two-layer conditional model which captures latent structure and estimates model parameters, jointly and optimally. We further expand its applicability by resorting to a weaker form of inference---maximum a-posteriori. The flexibility of the model is demonstrated on two structures based on total unimodularity---graph matching and linear chain. Experimental results confirm the promise of the method.

Matching users to the right items at the right time is a fundamental task in recommendation systems. As users interact with different items over time, users' and items' feature may evolve and co-evolve over time. Traditional models based on static latent features or discretizing time into epochs can become ineffective for capturing the fine-grained temporal dynamics in the user-item interactions. We propose a coevolutionary latent feature process model that accurately captures the coevolving nature of users' and items' feature. To learn parameters, we design an efficient convex optimization algorithm with a novel low rank space sharing constraints. Extensive experiments on diverse real-world datasets demonstrate significant improvements in user behavior prediction compared to state-of-the-arts.

Tensor networks are approximations of high-order tensors which are efficient to work with and have been very successful for physics and mathematics applications. We demonstrate how algorithms for optimizing tensor networks can be adapted to supervised learning tasks by using matrix product states (tensor trains) to parameterize non-linear kernel learning models. For the MNIST data set we obtain less than 1% test set classification error. We discuss an interpretation of the additional structure imparted by the tensor network to the learned model.

We present a framework for efficient inference in structured image models that explicitly reason about objects. We achieve this by performing probabilistic inference using a recurrent neural network that attends to scene elements and processes them one at a time. Crucially, the model itself learns to choose the appropriate number of inference steps. We use this scheme to learn to perform inference in partially specified 2D models (variable-sized variational auto-encoders) and fully specified 3D models (probabilistic renderers). We show that such models learn to identify multiple objects - counting, locating and classifying the elements of a scene - without any supervision, e.g., decomposing 3D images with various numbers of objects in a single forward pass of a neural network at unprecedented speed. We further show that the networks produce accurate inferences when compared to supervised counterparts, and that their structure leads to improved generalization.

Most learning algorithms are not invariant to the scale of the signal that is being approximated. We propose to adaptively normalize the targets used in the learning updates. This is important in value-based reinforcement learning, where the magnitude of appropriate value approximations can change over time when we update the policy of behavior. Our main motivation is prior work on learning to play Atari games, where the rewards were clipped to a predetermined range. This clipping facilitates learning across many different games with a single learning algorithm, but a clipped reward function can result in qualitatively different behavior. Using adaptive normalization we can remove this domain-specific heuristic without diminishing overall performance.

Maximum Mean Discrepancy (MMD) is a distance on the space of probability measures which has found numerous applications in machine learning and nonparametric testing. This distance is based on the notion of embedding probabilities in a reproducing kernel Hilbert space. In this paper, we present the first known lower bounds for the estimation of MMD based on finite samples. Our lower bounds hold for any radial universal kernel on $\R^d$ and match the existing upper bounds up to constants that depend only on the properties of the kernel. Using these lower bounds, we establish the minimax rate optimality of the empirical estimator and its $U$-statistic variant, which are usually employed in applications.

We propose the coupled generative adversarial nets (CoGAN) framework for generating pairs of corresponding images in two different domains. The framework consists of a pair of generative adversarial nets, each responsible for generating images in one domain. We show that by enforcing a simple weight-sharing constraint, the CoGAN learns to generate pairs of corresponding images without existence of any pairs of corresponding images in the two domains in the training set. In other words, the CoGAN learns a joint distribution of images in the two domains from images drawn separately from the marginal distributions of the individual domains. This is in contrast to the existing multi-modal generative models, which require corresponding images for training. We apply the CoGAN to several pair image generation tasks. For each task, the CoGAN learns to generate convincing pairs of corresponding images. We further demonstrate the applications of the CoGAN framework for the domain adaptation and cross-domain image generation tasks.

We describe a novel optimization method for finite sums (such as empirical risk minimization problems) building on the recently introduced SAGA method. Our method achieves an accelerated convergence rate on strongly convex smooth problems. Our method has only one parameter (a step size), and is radically simpler than other accelerated methods for finite sums. Additionally it can be applied when the terms are non-smooth, yielding a method applicable in many areas where operator splitting methods would traditionally be applied.

We investigate active learning with access to two distinct oracles: LABEL (which is standard) and SEARCH (which is not). The SEARCH oracle models the situation where a human searches a database to seed or counterexample an existing solution. SEARCH is stronger than LABEL while being natural to implement in many situations. We show that an algorithm using both oracles can provide exponentially large problem-dependent improvements over LABEL alone.

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.