Andrew J. Bean

Mutual information and time-interleaved analog-to-digital conversion

Analog to digital conversion is often a critical component of a digital communication link. However, the figures of merit that are used in the design of the components that comprise this step are more appropriate for signal reconstruction applications than for digital communication. This paper considers the design of time-interleaved analog-to-digital converters using the mutual information between the transmitted symbols and the outputs of the paths of the converter as a design criteria. Specific attention is paid to the sensitivity of the mutual information through the converter as a function of the relative sampling phases of the time-interleaved samplers. Mutual information is evaluated for a variety of converter strategies, channel conditions, and noise sources. It is shown that for oversampling converters, the optimal sampling phases not in general equispaced, as is conventionally assumed in converter design.

Factor graph switching portfolios under transaction costs

We consider the sequential portfolio investment problem. Building on results in signal processing, machine learning, and other areas, we use factor graphs to develop new universal portfolio algorithms for switching strategies under transaction costs. These algorithms make use of a transition diagram in order to compactly represent and compute message passing on an exponentially increasing number of factor graphs. We compare this with a previous universal switching portfolios, demonstrating typically superior performance.

Universal switching and side information portfolios under transaction costs using factor graphs

We consider the sequential portfolio investment problem. We combine various insights from universal portfolios research in order to construct more sophisticated algorithms that take into account transaction costs. In particular, we use the insights of Blum and Kalais transaction costs algorithm to take these costs into account in Cover and Ordentlichs side information portfolio and Kozat and Singers switching portfolio. This involves carefully designing a set of causal portfolio strategies and computing a convex combination of these according to a carefully designed distribution. Universal (sublinear regret) performance bounds for each of these portfolios show that the algorithms asymptotically achieve the wealth of the best strategy from the corresponding portfolio strategy set, to first order in the exponent. Factor graph representations of the algorithms demonstrate that computationally feasible algorithms may be derived. Finally, we present results of simulations of our algorithms and compare them to other portfolios.

Factor graphs for universal portfolios

We consider the sequential portfolio investment problem. Building on results in signal processing, machine learning, and other areas, we combine the insights of Cover and Ordentlichs side information portfolio with those of Blum and Kalais transaction costs algorithm to construct one that performs well under transaction costs while taking advantage of side information. We introduce factor graphs as a computational tool for analysis and design of universal (low regret) algorithms, and develop our algorithm with this insight. Finally, we demonstrate that, in contrast to other algorithms, our portfolio performs well over the full range of costs.

A tree-weighting approach to sequential decision problems with multiplicative loss

In this paper, we consider sequential decision problems in which the decision at each time is taken as a convex-combination of observations and whose performance metric is multiplicatively compounded over time. Such sequential decision problems arise in gambling, investing and in a host of signal processing applications from statistical language modeling to mixed-modality multimedia signal processing. Using a competitive algorithm framework, we construct sequential strategies that asymptotically achieve the performance of the best piecewise-convex strategy that could have been chosen by observing the entire sequence of outcomes in advance. Using the notion of context-trees, a mixture approach is able to asymptotically achieve the performance of the best choice of both the partitioning of the space of past observations and convex strategies within each region, for every sequence of outcomes. This performance is achieved with linear complexity in the depth of the context-tree, per decision. For the application of sequential investment, we also investigate transaction costs incurred for each decision. An explicit algorithmic description and examples demonstrating the performance of the algorithms are given. Our methods can be used to sequentially combine probability distributions produced by different statistical language models used in speech recognition or natural language processing and by different modalities in multimedia signal processing.

Universal portfolios via context trees

In this paper, we consider the sequential portfolio investment problem considered by Cover [3] and extend the results of [3] to the class of piecewise constant rebalanced portfolios that are tuned to the underlying sequence of price relatives. Here, the piecewise constant models are used to partition the space of past price relative vectors where we assign a different constant rebalanced portfolio to each region independently. We then extend these results where we compete against a doubly exponential number of piecewise constant portfolios that are represented by a context tree. We use the context tree to achieve the wealth of a portfolio selection algorithm that can choose both its partitioning of the space of the past price relatives and its constant rebalanced portfolio within each region of the partition, based on observing the entire sequence of price relatives in advance, uniformly, for every bounded deterministic sequence of price relative vectors. This performance is achieved with a portfolio algorithm whose complexity is only linear in the depth of the context tree per investment period. We demonstrate that the resulting portfolio algorithm achieves significant gains on historical stock pairs over the algorithm of [3] and the best constant rebalanced portfolio.

Universal Switching and Side Information Portfolios Under Transaction Costs Using Factor Graphs

We consider the sequential portfolio investment problem. We combine various insights from universal portfolios research in order to construct more sophisticated algorithms that take into account transaction costs. In particular, we use the insights of Blum and Kalais transaction costs algorithm to take these costs into account in Cover and Ordentlichs side information portfolio and Kozat and Singers switching portfolio. This involves carefully designing a set of causal portfolio strategies and computing a convex combination of these according to a carefully designed distribution. Universal (sublinear regret) performance bounds for each of these portfolios show that the algorithms asymptotically achieve the wealth of the best strategy from the corresponding portfolio strategy set, to first order in the exponent. Factor graph representations of the algorithms demonstrate that computationally feasible algorithms may be derived. Finally, we present results of simulations of our algorithms and compare them to other portfolios.

Portfolio selection via constrained stochastic gradients

In this paper, we consider the online portfolio selection problem. We develop several algorithms for portfolio selection based on sequential regularized optimizations and constrained stochastic gradient based approximations to this. We relate these methods to related results in stochastic gradients and universal portfolios, and compare results of simulations using historical data. We also demonstrate that these results compare favorably with respect to so-called universal portfolios.

Cooperative estimation in heterogeneous populations

We consider the problem of cooperative distributed estimation within a network of heterogeneous agents. We begin with the situation where each agent observes an independent stream of Bernoulli random variables, and the goal is for each to determine its own Bernoulli parameter. However, the agents of the population can be categorized into a small number of subgroups, where within each group the agents all have identical Bernoulli parameters. We present an algorithm for cooperative estimation in this setting which allows each agents estimate to asymptotically converge to the correct value. We show how our technique can be applied in other settings, such as in heterogeneous least mean squares filter populations. Finally, we present simulation results showing the benefit of our technique, and compare it to noncooperative parameter estimation in a Bernoulli population.

Experimental results with HF underwater acoustic modem for high bandwidth applications

We present a robust, video-capable modem designed for wireless underwater acoustic communication. The difficult nature of the underwater acoustic channel necessitates explicit Doppler compensation and mitigation of severe multipath. Due to the relatively low propagation speed of sound in water, platform mobility causes severe Doppler that cannot be treated as in RF wireless communicaiton, as a frequency shift or through a global rescaling. We model the underwater acoustic channel with explicit time-varying Doppler and multipath, and derive the turbo resampling equalizer (TRE) that tracks and mitigates these phenomena. Building on previous work, we demonstate experimental results achieving data rates in excess of 1 Mbps over 100 m in shallow water, and successfully transmit live video over a 5 m underwater acoustic channel from a rapidly moving transmitter with speeds in excess of 3 m/s and accelerations in excess of 7m/s2.