Randomized neural networks are immortalized in this AI Koan: In the days when Sussman was a novice, Minsky once came to him as he sat hacking at the PDP-6. ``What are you doing?'' asked Minsky. ``I am training a randomly wired neural net to play tic-tac-toe,'' Sussman replied. ``Why is the net wired randomly?'' asked Minsky. Sussman replied, ``I do not want it to have any preconceptions of how to play.'' Minsky then shut his eyes. ``Why do you close your eyes?'' Sussman asked his teacher. ``So that the room will be empty,'' replied Minsky. At that moment, Sussman was enlightened. We analyze shallow random networks with the help of concentration of measure inequalities. Specifically, we consider architectures that compute a weighted sum of their inputs after passing them through a bank of arbitrary randomized nonlinearities. We identify conditions under which these networks exhibit good classification performance, and bound their test error in terms of the size of the dataset and the number of random nonlinearities.

This paper describes a recursive estimation procedure for multivariate binary densities using orthogonal expansions. For $d$ covariates, there are $2^d$ basis coefficients to estimate, which renders conventional approaches computationally prohibitive when $d$ is large. However, for a wide class of densities that satisfy a certain sparsity condition, our estimator runs in probabilistic polynomial time and adapts to the unknown sparsity of the underlying density in two key ways: (1) it attains near-minimax mean-squared error, and (2) the computational complexity is lower for sparser densities. Our method also allows for flexible control of the trade-off between mean-squared error and computational complexity.

This paper studies global ranking problem by learning to rank methods. Conventional learning to rank methods are usually designed for `local ranking', in the sense that the ranking model is defined on a single object, for example, a document in information retrieval. For many applications, this is a very loose approximation. Relations always exist between objects and it is better to define the ranking model as a function on all the objects to be ranked (i.e., the relations are also included). This paper refers to the problem as global ranking and proposes employing a Continuous Conditional Random Fields (CRF) for conducting the learning task. The Continuous CRF model is defined as a conditional probability distribution over ranking scores of objects conditioned on the objects. It can naturally represent the content information of objects as well as the relation information between objects, necessary for global ranking. Taking two specific information retrieval tasks as examples, the paper shows how the Continuous CRF method can perform global ranking better than baselines.

We analyze the estimation of information theoretic measures of continuous random variables such as: differential entropy, mutual information or Kullback-Leibler divergence. The objective of this paper is two-fold. First, we prove that the information theoretic measure estimates using the k-nearest-neighbor density estimation with fixed k converge almost surely, even though the k-nearest-neighbor density estimation with fixed k does not converge to its true measure. Second, we show that the information theoretic measure estimates do not converge for k growing linearly with the number of samples. Nevertheless, these nonconvergent estimates can be used for solving the two-sample problem and assessing if two random variables are independent. We show that the two-sample and independence tests based on these nonconvergent estimates compare favorably with the maximum mean discrepancy test and the Hilbert Schmidt independence criterion, respectively.

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.

A series of corrections is developed for the fixed points of Expectation Propagation (EP),which is one of the most popular methods for approximate probabilistic inference. These corrections can lead to improvements of the inference approximation orserve as a sanity check, indicating when EP yields unrealiable results.

Theproblem of support union recovery is to recover the subset of covariates that are active in at least one of the regression problems.

The essence of exploration is acting to try to decrease uncertainty. We propose a new methodology for representing uncertainty in continuous-state control problems. Our approach, multi-resolution exploration (MRE), uses a hierarchical mapping to identify regions of the state space that would benefit from additional samples. We demonstrate MRE's broad utility by using it to speed up learning in a prototypical model-based and value-based reinforcement-learning method. Empirical results show that MRE improves upon state-of-the-art exploration approaches.

Bartlett et al (2006) recently proved that a ground condition for convex surrogates, classification calibration, ties up the minimization of the surrogates and classification risks, and left as an important problem the algorithmic questions about the minimization of these surrogates. In this paper, we propose an algorithm which provably minimizes any classification calibrated surrogate strictly convex and differentiable --- a set whose losses span the exponential, logistic and squared losses ---, with boosting-type guaranteed convergence rates under a weak learning assumption. A particular subclass of these surrogates, that we call balanced convex surrogates, has a key rationale that ties it to maximum likelihood estimation, zero-sum games and the set of losses that satisfy some of the most common requirements for losses in supervised learning. We report experiments on more than 50 readily available domains of 11 flavors of the algorithm, that shed light on new surrogates, and the potential of data dependent strategies to tune surrogates.

Kernel Principal Component Analysis (KPCA) is a popular generalization of linear PCA that allows non-linear feature extraction. In KPCA, data in the input space is mapped to higher (usually) dimensional feature space where the data can be linearly modeled. The feature space is typically induced implicitly by a kernel function, and linear PCA in the feature space is performed via the kernel trick. However, due to the implicitness of the feature space, some extensions of PCA such as robust PCA cannot be directly generalized to KPCA. This paper presents a technique to overcome this problem, and extends it to a unified framework for treating noise, missing data, and outliers in KPCA. Our method is based on a novel cost function to perform inference in KPCA. Extensive experiments, in both synthetic and real data, show that our algorithm outperforms existing methods.