When approximating binary similarity using the hamming distance between short binary hashes, we shown that even if the similarity is symmetric, we can have shorter and more accurate hashes by using two distinct code maps. I.e.~by approximating the similarity between $x$ and $x'$ as the hamming distance between $f(x)$ and $g(x')$, for two distinct binary codes $f,g$, rather than as the hamming distance between $f(x)$ and $f(x')$.

We consider the problem of embedding entities and relationships of multi-relational data in low-dimensional vector spaces. Our objective is to propose a canonical model which is easy to train, contains a reduced number of parameters and can scale up to very large databases. Hence, we propose, TransE, a method which models relationships by interpreting them as translations operating on the low-dimensional embeddings of the entities. Despite its simplicity, this assumption proves to be powerful since extensive experiments show that TransE significantly outperforms state-of-the-art methods in link prediction on two knowledge bases. Besides, it can be successfully trained on a large scale data set with 1M entities, 25k relationships and more than 17M training samples.

Psychologists are interested in developing instructional policies that boost student learning. An instructional policy specifies the manner and content of instruction. For example, in the domain of concept learning, a policy might specify the nature of exemplars chosen over a training sequence. Traditional psychological studies compare several hand-selected policies, e.g., contrasting a policy that selects only difficult-to-classify exemplars with a policy that gradually progresses over the training sequence from easy exemplars to more difficult (known as {\em fading}). We propose an alternative to the traditional methodology in which we define a parameterized space of policies and search this space to identify the optimum policy. For example, in concept learning, policies might be described by a fading function that specifies exemplar difficulty over time. We propose an experimental technique for searching policy spaces using Gaussian process surrogate-based optimization and a generative model of student performance. Instead of evaluating a few experimental conditions each with many human subjects, as the traditional methodology does, our technique evaluates many experimental conditions each with a few subjects. Even though individual subjects provide only a noisy estimate of the population mean, the optimization method allows us to determine the shape of the policy space and identify the global optimum, and is as efficient in its subject budget as a traditional A-B comparison. We evaluate the method via two behavioral studies, and suggest that the method has broad applicability to optimization problems involving humans in domains beyond the educational arena.

Many powerful Monte Carlo techniques for estimating partition functions, such as annealed importance sampling (AIS), are based on sampling from a sequence of intermediate distributions which interpolate between a tractable initial distribution and an intractable target distribution. The near-universal practice is to use geometric averages of the initial and target distributions, but alternative paths can perform substantially better. We present a novel sequence of intermediate distributions for exponential families: averaging the moments of the initial and target distributions. We derive an asymptotically optimal piecewise linear schedule for the moments path and show that it performs at least as well as geometric averages with a linear schedule. Moment averaging performs well empirically at estimating partition functions of restricted Boltzmann machines (RBMs), which form the building blocks of many deep learning models, including Deep Belief Networks and Deep Boltzmann Machines.

We use the notion of local Rademacher complexity to design new algorithms for learning kernels. Our algorithms thereby benefit from the sharper learning bounds based on that notion which, under certain general conditions, guarantee a faster convergence rate. We devise two new learning kernel algorithms: one based on a convex optimization problem for which we give an efficient solution using existing learning kernel techniques, and another one that can be formulated as a DC-programming problem for which we describe a solution in detail. We also report the results of experiments with both algorithms in both binary and multi-class classification tasks.

A common classifier for unlabeled nodes on undirected graphs uses label propagation from the labeled nodes, equivalent to the harmonic predictor on Gaussian random fields (GRFs). For active learning on GRFs, the commonly used V-optimality criterion queries nodes that reduce the L2 (regression) loss. V-optimality satisfies a submodularity property showing that greedy reduction produces a (1 − 1/e) globally optimal solution. However, L2 loss may not characterise the true nature of 0/1 loss in classification problems and thus may not be the best choice for active learning. We consider a new criterion we call Σ-optimality, which queries the node that minimizes the sum of the elements in the predictive covariance. Σ-optimality directly optimizes the risk of the surveying problem, which is to determine the proportion of nodes belonging to one class. In this paper we extend submodularity guarantees from V-optimality to Σ-optimality using properties specific to GRFs. We further show that GRFs satisfy the suppressor-free condition in addition to the conditional independence inherited from Markov random fields. We test Σ-optimality on real-world graphs with both synthetic and real data and show that it outperforms V-optimality and other related methods on classification.

We investigate three related and important problems connected to machine learning, namely approximating a submodular function everywhere, learning a submodular function (in a PAC like setting [26]), and constrained minimization of submodular functions. In all three problems, we provide improved bounds which depend on the “curvature” of a submodular function and improve on the previously known best results for these problems [9, 3, 7, 25] when the function is not too curved – a property which is true of many real-world submodular functions. In the former two problems, we obtain these bounds through a generic black-box transformation (which can potentially work for any algorithm), while in the case of submodular minimization, we propose a framework of algorithms which depend on choosing an appropriate surrogate for the submodular function. In all these cases, we provide almost matching lower bounds. While improved curvature-dependent bounds were shown for monotone submodular maximization [4, 27], the existence of similar improved bounds for the aforementioned problems has been open. We resolve this question in this paper by showing that the same notion of curvature provides these improved results. Empirical experiments add further support to our claims.

We design and analyze minimax-optimal algorithms for online linear optimization games where the player's choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark strategy. The standard benchmark is the loss of the best strategy chosen from a bounded comparator set, whereas we consider a broad range of benchmark functions. We consider the problem as a sequential multi-stage zero-sum game, and we give a thorough analysis of the minimax behavior of the game, providing characterizations for the value of the game, as well as both the player's and the adversary's optimal strategy. We show how these objects can be computed efficiently under certain circumstances, and by selecting an appropriate benchmark, we construct a novel hedging strategy for an unconstrained betting game.

In this paper we propose a class of efficient Generalized Method-of-Moments(GMM) algorithms for computing parameters of the Plackett-Luce model, where the data consists of full rankings over alternatives. Our technique is based on breaking the full rankings into pairwise comparisons, and then computing parameters that satisfy a set of generalized moment conditions. We identify conditions for the output of GMM to be unique, and identify a general class of consistent and inconsistent breakings. We then show by theory and experiments that our algorithms run significantly faster than the classical Minorize-Maximization (MM) algorithm, while achieving competitive statistical efficiency.

Maximization of submodular functions has wide applications in machine learning and artificial intelligence. Adaptive submodular maximization has been traditionally studied under the assumption that the model of the world, the expected gain of choosing an item given previously selected items and their states, is known. In this paper, we study the scenario where the expected gain is initially unknown and it is learned by interacting repeatedly with the optimized function. We propose an efficient algorithm for solving our problem and prove that its expected cumulative regret increases logarithmically with time. Our regret bound captures the inherent property of submodular maximization, earlier mistakes are more costly than later ones. We refer to our approach as Optimistic Adaptive Submodular Maximization (OASM) because it trades off exploration and exploitation based on the optimism in the face of uncertainty principle. We evaluate our method on a preference elicitation problem and show that non-trivial K-step policies can be learned from just a few hundred interactions with the problem.