Starting with the work of Jaakkola and Haussler, a variety of approaches have been proposed for coupling domain-specific generative models with statistical learning methods. The link is established by a kernel function which provides a similarity measure based inherently on the underlying model. In computational biology, the full promise of this framework has rarely ever been exploited, as most kernels are derived from very generic models, such as sequence profiles or hidden Markov models. Here, we introduce the MTreeMix kernel, which is based on a generative model tailored to the underlying biological mechanism.

We study the problem of parameter estimation in continuous density hidden Markov models (CD-HMMs) for automatic speech recognition (ASR). As in support vectormachines, we propose a learning algorithm based on the goal of margin maximization. Unlike earlier work on max-margin Markov networks, our approach is specifically geared to the modeling of real-valued observations (such as acoustic feature vectors) using Gaussian mixture models. Unlike previous discriminative frameworksfor ASR, such as maximum mutual information and minimum classification error, our framework leads to a convex optimization, without any spurious local minima. The objective function for large margin training of CD-HMMs is defined over a parameter space of positive semidefinite matrices. Its optimization can be performed efficiently with simple gradient-based methods thatscale well to large problems. We obtain competitive results for phonetic recognition on the TIMIT speech corpus.

We describe Hidden Semi-Markov Support Vector Machines (SHM SVMs), an extension of HM SVMs to semi-Markov chains. This allows us to predict segmentations ofsequences based on segment-based features measuring properties such as the length of the segment. We propose a novel technique to partition the problem into sub-problems. The independently obtained partial solutions can then be recombined in an efficient way, which allows us to solve label sequence learning problemswith several thousands of labeled sequences. We have tested our algorithm for predicting gene structures, an important problem in computational biology. Results on a well-known model organism illustrate the great potential of SHM SVMs in computational biology.

Scoring structures of undirected graphical models by means of evaluating the marginal likelihood is very hard. The main reason is the presence of the partition functionwhich is intractable to evaluate, let alone integrate over. We propose to approximate the marginal likelihood by employing two levels of approximation: we assume normality of the posterior (the Laplace approximation) and approximate allremaining intractable quantities using belief propagation and the linear response approximation.

We rigorously establish a close relationship between message passing algorithms and models of neurodynamics by showing that the equations of a continuous Hopfield networkcan be derived from the equations of belief propagation on a binary Markov random field. As Hopfield networks are equipped with a Lyapunov function, convergenceis guaranteed. As a consequence, in the limit of many weak connections perneuron, Hopfield networks exactly implement a continuous-time variant of belief propagation starting from message initialisations that prevent from running into convergence problems. Our results lead to a better understanding of the role of message passing algorithms in real biological neural networks.

The local statistical properties of photographic images, when represented in a multi-scale basis, have been described using Gaussian scale mixtures (GSMs). Here, we use this local description to construct a global field of Gaussian scale mixtures (FoGSM).

Markov networks are commonly used in a wide variety of applications, ranging from computer vision, to natural language, to computational biology. In most current applications, even those that rely heavily on learned models, the structure of the Markov network is constructed by hand, due to the lack of effective algorithms forlearning Markov network structure from data. In this paper, we provide a computationally efficient method for learning Markov network structure from data.

Everyday inductive reasoning draws on many kinds of knowledge, including knowledge about relationships between properties and knowledge about relationships between objects. Previous accounts of inductive reasoning generally focus on just one kind of knowledge: models of causal reasoning often focus on relationships between properties, and models of similarity-based reasoning often focus on similarity relationships between objects. We present a Bayesian model of inductive reasoning that incorporates both kinds of knowledge, and show that it accounts well for human inferences about the properties of biological species.

Their machine counterparts have historically been unable to compete with this ability, until now.

Learning by imitation represents an important mechanism for rapid acquisition of new behaviors in humans and robots. A critical requirement for learning by imitation is the ability to handle uncertainty arising from the observation process as well as the imitator's own dynamics and interactions with the environment. In this paper, we present a new probabilistic method for inferring imitative actions that takes into account both the observations of the teacher as well as the imitator's dynamics. Our key contribution is a nonparametric learning method which generalizes to systems with very different dynamics. Rather than relying on a known forward model of the dynamics, our approach learns a nonparametric forward model via exploration. Leveraging advances in approximate inference in graphical models, we show how the learned forward model can be directly used to plan an imitating sequence. We provide experimental results for two systems: a biome-chanical model of the human arm and a 25-degrees-of-freedom humanoid robot. We demonstrate that the proposed method can be used to learn appropriate motor inputs to the model arm which imitates the desired movements. A second set of results demonstrates dynamically stable full-body imitation of a human teacher by the humanoid robot.