The constraint satisfaction problem (CSP) is a general problem central to computer science and artificial intelligence. Although the CSP is NP-hard in general, considerable effort has been spent on identifying tractable subclasses. The main two approaches consider structural properties (restrictions on the hypergraph of constraint scopes) and relational properties (restrictions on the language of constraint relations). Recently, some authors have considered hybrid properties that restrict the constraint hypergraph and the relations simultaneously. Our key contribution is the novel concept of a CSP pattern and classes of problems defined by forbidden patterns (which can be viewed as forbidding generic subproblems). We describe the theoretical framework which can be used to reason about classes of problems defined by forbidden patterns. We show that this framework generalises relational properties and allows us to capture known hybrid tractable classes. Although we are not close to obtaining a dichotomy concerning the tractability of general forbidden patterns, we are able to make some progress in a special case: classes of problems that arise when we can only forbid binary negative patterns (generic subproblems in which only inconsistent tuples are specified). In this case we are able to characterise very large classes of tractable and NP-hard forbidden patterns. This leaves the complexity of just one case unresolved and we conjecture that this last case is tractable.

We consider the problem of learning overcomplete dictionaries in the context of sparse coding, where each sample selects a sparse subset of dictionary elements. Our main result is a strategy to approximately recover the unknown dictionary using an efficient algorithm. Our algorithm is a clustering-style procedure, where each cluster is used to estimate a dictionary element. The resulting solution can often be further cleaned up to obtain a high accuracy estimate, and we provide one simple scenario where $\ell_1$-regularized regression can be used for such a second stage.

We perform the first study of the tradeoff space of access methods and replication to support statistical analytics using first-order methods executed in the main memory of a Non-Uniform Memory Access (NUMA) machine. Statistical analytics systems differ from conventional SQL-analytics in the amount and types of memory incoherence they can tolerate. Our goal is to understand tradeoffs in accessing the data in row- or column-order and at what granularity one should share the model and data for a statistical task. We study this new tradeoff space, and discover there are tradeoffs between hardware and statistical efficiency. We argue that our tradeoff study may provide valuable information for designers of analytics engines: for each system we consider, our prototype engine can run at least one popular task at least 100x faster. We conduct our study across five architectures using popular models including SVMs, logistic regression, Gibbs sampling, and neural networks.

The success of machine learning on a given task dependson, among other things, which learning algorithm is selected and its associated hyperparameters. Selecting an appropriate learning algorithm and setting its hyperparameters for a given data set can be a challenging task, especially for users who are not experts in machine learning. Previous work has examined using meta-features to predict which learning algorithm and hyperparameters should be used. However, choosing a set of meta-features that are predictive of algorithm performance is difficult. Here, we propose to apply collaborative filtering techniques to learning algorithm and hyperparameter selection, and find that doing so avoids determining which meta-features to use and outperforms traditional meta-learning approaches in many cases.

In this paper we propose and study a family of sparsity-inducing penalty functions. Since the penalty functions are related to the kinetic energy in special relativity, we call them \emph{kinetic energy plus} (KEP) functions. We construct the KEP function by using the concave conjugate of a $\chi^2$-distance function and present several novel insights into the KEP function with $q=1$. In particular, we derive a thresholding operator based on the KEP function, and prove its mathematical properties and asymptotic properties in sparsity modeling. Moreover, we show that a coordinate descent algorithm is especially appropriate for the KEP function. Additionally, we discuss the relationship of KEP with the penalty functions $\ell_{1/2}$ and MCP. The theoretical and empirical analysis validates that the KEP function is effective and efficient in high-dimensional data modeling.

Today there's no legislation regarding how much intelligence a machine can have, how interconnected it can be. If that continues, look at the exponential trend. We will reach the singularity in the timeframe most experts predict. From that point on you're going to see that the top species will no longer be humans, but machines.

Finding statistically significant interactions between binary variables is computationally and statistically challenging in high-dimensional settings, due to the combinatorial explosion in the number of hypotheses. Terada et al. recently showed how to elegantly address this multiple testing problem by excluding non-testable hypotheses. Still, it remains unclear how their approach scales to large datasets. We here proposed strategies to speed up the approach by Terada et al. and evaluate them thoroughly in 11 real-world benchmark datasets. We observe that one approach, incremental search with early stopping, is orders of magnitude faster than the current state-of-the-art approach.

Recently, multiple formulations of vision problems as probabilistic inversions of generative models based on computer graphics have been proposed. However, applications to 3D perception from natural images have focused on low-dimensional latent scenes, due to challenges in both modeling and inference. Accounting for the enormous variability in 3D object shape and 2D appearance via realistic generative models seems intractable, as does inverting even simple versions of the many-to-many computations that link 3D scenes to 2D images. This paper proposes and evaluates an approach that addresses key aspects of both these challenges. We show that it is possible to solve challenging, real-world 3D vision problems by approximate inference in generative models for images based on rendering the outputs of probabilistic CAD (PCAD) programs. Our PCAD object geometry priors generate deformable 3D meshes corresponding to plausible objects and apply affine transformations to place them in a scene. Image likelihoods are based on similarity in a feature space based on standard mid-level image representations from the vision literature. Our inference algorithm integrates single-site and locally blocked Metropolis-Hastings proposals, Hamiltonian Monte Carlo and discriminative data-driven proposals learned from training data generated from our models. We apply this approach to 3D human pose estimation and object shape reconstruction from single images, achieving quantitative and qualitative performance improvements over state-of-the-art baselines.

Modeling videos and image-sets as linear subspaces has proven beneficial for many visual recognition tasks. However, it also incurs challenges arising from the fact that linear subspaces do not obey Euclidean geometry, but lie on a special type of Riemannian manifolds known as Grassmannian. To leverage the techniques developed for Euclidean spaces (e.g, support vector machines) with subspaces, several recent studies have proposed to embed the Grassmannian into a Hilbert space by making use of a positive definite kernel. Unfortunately, only two Grassmannian kernels are known, none of which -as we will show- is universal, which limits their ability to approximate a target function arbitrarily well. Here, we introduce several positive definite Grassmannian kernels, including universal ones, and demonstrate their superiority over previously-known kernels in various tasks, such as classification, clustering, sparse coding and hashing.

Recommendation systems have been integrated into the majority of large online systems. They tailor those systems to individual users by filtering and ranking information according to user profiles. This adaptation process influences the way users interact with the system and, as a consequence, increases the difficulty of evaluating a recommendation algorithm with historical data (via offline evaluation). This paper analyses this evaluation bias and proposes a simple item weighting solution that reduces its impact. The efficiency of the proposed solution is evaluated on real world data extracted from Viadeo professional social network.