UNIFYING PROBABILISTIC MODELS FOR TIME-FREQUENCY ANALYSIS

In audio signal processing, probabilistic time-frequency models have many benefits over their non-probabilistic counterparts. They adapt to the incoming signal, quantify uncertainty, and measure correlation between the signal's amplitude and phase information, making time domain resynthesis straightforward. However, these models are still not widely used since they come at a high computational cost, and because they are formulated in such a way that it can be difficult to interpret all the modelling assumptions. By showing their equivalence to Spectral Mixture Gaussian processes, we illuminate the underlying model assumptions and provide a general framework for constructing more complex models that better approximate real-world signals. Our interpretation makes it intuitive to inspect, compare, and alter the models since all prior knowledge is encoded in the Gaussian process kernel functions. We utilise a state space representation to perform efficient inference via Kalman smoothing, and we demonstrate how our interpretation allows for efficient parameter learning in the frequency domain.Comment: Accepted to International Conference on Acoustics, Speech and Signal Processing (ICASSP) 201

Unifying Two Views on Multiple Mean-Payoff Objectives in Markov Decision Processes

We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives. There exist two different views: (i) the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector. We consider optimization with respect to both objectives at once, thus unifying the existing semantics. Precisely, the goal is to optimize the expectation while ensuring the satisfaction constraint. Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., ensure certain probabilistic guarantee). Our main results are as follows: First, we present algorithms for the decision problems which are always polynomial in the size of the MDP. We also show that an approximation of the Pareto-curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions. Second, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.Comment: Extended journal version of the LICS'15 pape

Neural Mechanisms for Information Compression by Multiple Alignment, Unification and Search

This article describes how an abstract framework for perception and cognition may be realised in terms of neural mechanisms and neural processing. This framework — called information compression by multiple alignment, unification and search (ICMAUS) — has been developed in previous research as a generalized model of any system for processing information, either natural or artificial. It has a range of applications including the analysis and production of natural language, unsupervised inductive learning, recognition of objects and patterns, probabilistic reasoning, and others. The proposals in this article may be seen as an extension and development of Hebb’s (1949) concept of a ‘cell assembly’. The article describes how the concept of ‘pattern’ in the ICMAUS framework may be mapped onto a version of the cell assembly concept and the way in which neural mechanisms may achieve the effect of ‘multiple alignment’ in the ICMAUS framework. By contrast with the Hebbian concept of a cell assembly, it is proposed here that any one neuron can belong in one assembly and only one assembly. A key feature of present proposals, which is not part of the Hebbian concept, is that any cell assembly may contain ‘references’ or ‘codes’ that serve to identify one or more other cell assemblies. This mechanism allows information to be stored in a compressed form, it provides a robust mechanism by which assemblies may be connected to form hierarchies and other kinds of structure, it means that assemblies can express abstract concepts, and it provides solutions to some of the other problems associated with cell assemblies. Drawing on insights derived from the ICMAUS framework, the article also describes how learning may be achieved with neural mechanisms. This concept of learning is significantly different from the Hebbian concept and appears to provide a better account of what we know about human learning

Decision by sampling

We present a theory of decision by sampling (DbS) in which, in contrast with traditional models, there are no underlying psychoeconomic scales. Instead, we assume that an attribute’s subjective value is constructed from a series of binary, ordinal comparisons to a sample of attribute values drawn from memory and is its rank within the sample. We assume that the sample reflects both the immediate distribution of attribute values from the current decision’s context and also the background, real-world distribution of attribute values. DbS accounts for concave utility functions; losses looming larger than gains; hyperbolic temporal discounting; and the overestimation of small probabilities and the underestimation of large probabilities