Motivated from real world problems, like object categorization, we study a particular mixed-norm regularization for Multiple Kernel Learning (MKL). It is assumed that the given set of kernels are grouped into distinct components where each component is crucial for the learning task at hand. The formulation hence employs $l_\infty$ regularization for promoting combinations at the component level and $l_1$ regularization for promoting sparsity among kernels in each component. While previous attempts have formulated this as a non-convex problem, the formulation given here is an instance of non-smooth convex optimization problem which admits an efficient Mirror-Descent (MD) based procedure. The MD procedure optimizes over product of simplexes, which is not a well-studied case in literature. Results on real-world datasets show that the new MKL formulation is well-suited for object categorization tasks and that the MD based algorithm outperforms state-of-the-art MKL solvers like \texttt{simpleMKL} in terms of computational effort.

We are often interested in casting classification and clustering problems in a regression framework, because it is feasible to achieve some statistical properties in this framework by imposing some penalty criteria. In this paper we illustrate optimal scoring, which was originally proposed for performing Fisher linear discriminant analysis by regression, in the application of unsupervised learning. In particular, we devise a novel clustering algorithm that we call optimal discriminant clustering (ODC). We associate our algorithm with the existing unsupervised learning algorithms such as spectral clustering, discriminative clustering and sparse principal component analysis. Thus, our work shows that optimal scoring provides a new approach to the implementation of unsupervised learning. This approach facilitates the development of new unsupervised learning algorithms.

Causal structure-discovery techniques usually assume that all causes of more than one variable are observed. This is the so-called causal sufficiency assumption. In practice, it is untestable, and often violated. In this paper, we present an efficient causal structure-learning algorithm, suited for causally insufficient data. Similar to algorithms such as IC* and FCI, the proposed approach drops the causal sufficiency assumption and learns a structure that indicates (potential) latent causes for pairs of observed variables. Assuming a constant local density of the data-generating graph, our algorithm makes a quadratic number of conditional-independence tests w.r.t. the number of variables. We show with experiments that our algorithm is comparable to the state-of-the-art FCI algorithm in accuracy, while being several orders of magnitude faster on large problems. We conclude that MBCS* makes a new range of causally insufficient problems computationally tractable.

Semantic hashing seeks compact binary codes of datapoints so that the Hamming distance between codewords correlates with semantic similarity. Hinton et al. used a clever implementation of autoencoders to find such codes. In this paper, we show that the problem of finding a best code for a given dataset is closely related to the problem of graph partitioning and can be shown to be NP hard. By relaxing the original problem, we obtain a spectral method whose solutions are simply a subset of thresh- olded eigenvectors of the graph Laplacian. By utilizing recent results on convergence of graph Laplacian eigenvectors to the Laplace-Beltrami eigen- functions of manifolds, we show how to efficiently calculate the code of a novel datapoint. Taken together, both learning the code and applying it to a novel point are extremely simple. Our experiments show that our codes significantly outperform the state-of-the art.

We use graphical models and structure learning to explore how people learn policies in sequential decision making tasks. Studies of sequential decision-making in humans frequently find suboptimal performance relative to an ideal actor that knows the graph model that generates reward in the environment. We argue that the learning problem humans face also involves learning the graph structure for reward generation in the environment. We formulate the structure learning problem using mixtures of reward models, and solve the optimal action selection problem using Bayesian Reinforcement Learning. We show that structure learning in one and two armed bandit problems produces many of the qualitative behaviors deemed suboptimal in previous studies. Our argument is supported by the results of experiments that demonstrate humans rapidly learn and exploit new reward structure.

We consider the problem of bounding from above the log-partition function corresponding to second-order Ising models for binary distributions. We introduce a new bound, the cardinality bound, which can be computed via convex optimization. The corresponding error on the logpartition functionis bounded above by twice the distance, in model parameter space, to a class of "standard" Ising models, for which variable interdependence is described via a simple mean field term. In the context of maximum-likelihood, using the new bound instead of the exact log-partition function, while constraining the distance to the class of standard Ising models, leads not only to a good approximation to the log-partition function, but also to a model that is parsimonious, and easily interpretable.We compare our bound with the log-determinant bound introduced by Wainwright and Jordan (2006), and show that when the l

We develop a probabilistic model of human memory performance in free recall experiments. In these experiments, a subject first studies a list of words and then tries to recall them. To model these data, we draw on both previous psychological research and statistical topic models of text documents. We assume that memories are formed by assimilating the semantic meaning of studied words (represented as a distribution over topics) into a slowly changing latent context (represented in the same space). During recall, this context is reinstated and used as a cue for retrieving studied words. By conceptualizing memory retrieval as a dynamic latent variable model, we are able to use Bayesian inference to represent uncertainty and reason about the cognitive processes underlying memory. We present a particle filter algorithm for performing approximate posterior inference, and evaluate our model on the prediction of recalled words in experimental data. By specifying the model hierarchically, we are also able to capture inter-subject variability.

We present a sparse approximation approach for dependent output Gaussian processes (GP). Employing a latent function framework, we apply the convolution process formalism to establish dependencies between output variables, where each latent function is represented as a GP. Based on these latent functions, we establish an approximation scheme using a conditional independence assumption between the output processes, leading to an approximation of the full covariance which is determined by the locations at which the latent functions are evaluated. We show results of the proposed methodology for synthetic data and real world applications on pollution prediction and a sensor network.

Regularized risk minimization often involves non-smooth optimization, either because of the loss function (e.g., hinge loss) or the regularizer (e.g., $\ell_1$-regularizer). Gradient descent methods, though highly scalable and easy to implement, are known to converge slowly on these problems. In this paper, we develop novel accelerated gradient methods for stochastic optimization while still preserving their computational simplicity and scalability. The proposed algorithm, called SAGE (Stochastic Accelerated GradiEnt), exhibits fast convergence rates on stochastic optimization with both convex and strongly convex objectives. Experimental results show that SAGE is faster than recent (sub)gradient methods including FOLOS, SMIDAS and SCD. Moreover, SAGE can also be extended for online learning, resulting in a simple but powerful algorithm.

The use of context is critical for scene understanding in computer vision, where the recognition of an object is driven by both local appearance and the objects relationship to other elements of the scene (context). Most current approaches rely on modeling the relationships between object categories as a source of context. In this paper we seek to move beyond categories to provide a richer appearance-based model of context. We present an exemplar-based model of objects and their relationships, the Visual Memex, that encodes both local appearance and 2D spatial context between object instances. We evaluate our model on Torralbas proposed Context Challenge against a baseline category-based system. Our experiments suggest that moving beyond categories for context modeling appears to be quite beneficial, and may be the critical missing ingredient in scene understanding systems.