In this article, we propose fast subtree kernels on graphs.

We consider multi-label prediction problems with large output spaces under the assumption of output sparsity - that the target (label) vectors have small support. We develop a general theory for a variant of the popular error correcting output code scheme, using ideas from compressed sensing for exploiting this sparsity. The method can be regarded as a simple reduction from multi-label regression problems to binary regression problems. We show that the number of subproblems need only be logarithmic in the total number of possible labels, making this approach radically more efficient than others. We also state and prove robustness guarantees for this method in the form of regret transform bounds (in general), and also provide a more detailed analysis for the linear prediction setting.

CAPTCHAs are computer-generated tests that humans can pass but current computer systems cannot. CAPTCHAs provide a method for automatically distinguishing a human from a computer program, and therefore can protect Web services from abuse by so-called "bots." Most CAPTCHAs consist of distorted images, usually text, for which a user must provide some description. Unfortunately, visual CAPTCHAs limit access to the millions of visually impaired people using the Web. Audio CAPTCHAs were created to solve this accessibility issue; however, the security of audio CAPTCHAs was never formally tested.

Embeddings of random variables in reproducing kernel Hilbert spaces (RKHSs) may be used to conduct statistical inference based on higher order moments. For sufficiently rich (characteristic) RKHSs, each probability distribution has a unique embedding, allowing all statistical properties of the distribution to be taken into consideration. Necessary and sufficient conditions for an RKHS to be characteristic exist for $\R^n$. In the present work, conditions are established for an RKHS to be characteristic on groups and semigroups. Illustrative examples are provided, including characteristic kernels on periodic domains, rotation matrices, and $\R^n_+$.

We study the profit-maximization problem of a monopolistic market-maker who sets two-sided prices in an asset market. The sequential decision problem is hard to solve because the state space is a function. We demonstrate that the belief state is well approximated by a Gaussian distribution. We prove a key monotonicity property of the Gaussian state update which makes the problem tractable, yielding the first optimal sequential market-making algorithm in an established model. The algorithm leads to a surprising insight: an optimal monopolist can provide more liquidity than perfectly competitive market-makers in periods of extreme uncertainty, because a monopolist is willing to absorb initial losses in order to learn a new valuation rapidly so she can extract higher profits later.

This paper presents a spike feature extraction algorithm that targets real-time spike sorting and facilitates miniaturized microchip implementation. The proposed algorithm has been evaluated on synthesized waveforms and experimentally recorded sequences. When compared with many spike sorting approaches our algorithm demonstrates improved speed, accuracy and allows unsupervised execution. A preliminary hardware implementation has been realized using an integrated microchip interfaced with a personal computer.

We consider the problem of finding the M assignments with maximum probability in a probabilistic graphical model. We show how this problem can be formulated as a linear program (LP) on a particular polytope. We prove that, for tree graphs (and junction trees in general), this polytope has a particularly simple form and differs from the marginal polytope in a single inequality constraint. We use this characterization to provide an approximation scheme for non-tree graphs, by using the set of spanning trees over such graphs. The method we present puts the M-best inference problem in the context of LP relaxations, which have recently received considerable attention and have proven useful in solving difficult inference problems.

We consider the problem of finding the M assignments with maximum probability in a probabilistic graphical model. We show how this problem can be formulated as a linear program (LP) on a particular polytope. We prove that, for tree graphs (and junction trees in general), this polytope has a particularly simple form and differs from the marginal polytope in a single inequality constraint. We use this characterization to provide an approximation scheme for non-tree graphs, by using the set of spanning trees over such graphs. The method we present puts the M-best inference problem in the context of LP relaxations, which have recently received considerable attention and have proven useful in solving difficult inference problems.

Inspired by the hierarchical hidden Markov models (HHMM), we present the hierarchical semi-Markov conditional random field (HSCRF), a generalisation of embedded undirected Markov chains to model complex hierarchical, nested Markov processes. It is parameterised in a discriminative framework and has polynomial time algorithms for learning and inference. Importantly, we develop efficient algorithms for learning and constrained inference in a partially-supervised setting, which is important issue in practice where labels can only be obtained sparsely. We demonstrate the HSCRF in two applications: (i) recognising human activities of daily living (ADLs) from indoor surveillance cameras, and (ii) noun-phrase chunking. We show that the HSCRF is capable of learning rich hierarchical models with reasonable accuracy in both fully and partially observed data cases.

CAPTCHAs are computer-generated tests that humans can pass but current computer systems cannot. CAPTCHAs provide a method for automatically distinguishing a human from a computer program, and therefore can protect Web services from abuse by so-called "bots." Most CAPTCHAs consist of distorted images, usually text, for which a user must provide some description. Unfortunately, visual CAPTCHAs limit access to the millions of visually impaired people using the Web. Audio CAPTCHAs were created to solve this accessibility issue; however, the security of audio CAPTCHAs was never formally tested.