Phebe Vayanos

Collaborative Adaptive Learning using Hybrid Filters

A novel stable and robust algorithm for training of finite impulse response adaptive filters is proposed. This is achieved based on a convex combination of the least mean square (LMS) and a recently proposed generalised normalised gradient descent (GNGD) algorithm. In this way, the desirable fast convergence and stability of GNGD is combined with the robustness and small steady state misadjustment of LMS. Simulations on linear and nonlinear signals in the prediction setting support the analysis.

A constraint sampling approach for multi-stage robust optimization

We propose a tractable approximation scheme for convex (not necessarily linear) multi-stage robust optimization problems. We approximate the adaptive decisions by finite linear combinations of prescribed basis functions and demonstrate how one can optimize over these decision rules at low computational cost through constraint randomization. We obtain a-priori probabilistic guarantees on the feasibility properties of the optimal decision rule by applying existing constraint sampling techniques to the semi-infinite problem arising from the decision rule approximation. We demonstrate that for a suitable choice of basis functions, the approximation converges as the size of the basis and the number of sampled constraints tend to infinity. The approach yields an algorithm parameterized in the basis size, the probability of constraint violation and the confidence that this probability will not be exceeded. These three parameters serve to tune the trade-off between optimality and feasibility of the decision rules and the computational cost of the algorithm. We assess the convergence and scalability properties of our approach in the context of two inventory management problems.

Decision rules for information discovery in multi-stage stochastic programming

Stochastic programming and robust optimization are disciplines concerned with optimal decision-making under uncertainty over time. Traditional models and solution algorithms have been tailored to problems where the order in which the uncertainties unfold is independent of the controller actions. Nevertheless, in numerous real-world decision problems, the time of information discovery can be influenced by the decision maker, and uncertainties only become observable following an (often costly) investment. Such problems can be formulated as mixed-binary multi-stage stochastic programs with decision-dependent non-anticipativity constraints. Unfortunately, these problems are severely computationally intractable. We propose an approximation scheme for multi-stage problems with decision-dependent information discovery which is based on techniques commonly used in modern robust optimization. In particular, we obtain a conservative approximation in the form of a mixed-binary linear program by restricting the spaces of measurable binary and real-valued decision rules to those that are representable as piecewise constant and linear functions of the uncertain parameters, respectively. We assess our approach on a problem of infrastructure and production planning in offshore oil fields from the literature.

Characterisation of Signal Modality: Exploiting Signal Nonlinearity in Machine Learning and Signal Processing

A novel method for online tracking of the changes in the nonlinearity within both real-domain and complex–valued signals is introduced. This is achieved by a collaborative adaptive signal processing approach based on a hybrid filter. By tracking the dynamics of the adaptive mixing parameter within the employed hybrid filtering architecture, we show that it is possible to quantify the degree of nonlinearity within both real- and complex-valued data. Implementations for tracking nonlinearity in general and then more specifically sparsity are illustrated on both benchmark and real world data. It is also shown that by combining the information obtained from hybrid filters of different natures it is possible to use this method to gain a more complete understanding of the nature of the nonlinearity within a signal. This also paves the way for building multidimensional feature spaces and their application in data/information fusion.

Online tracking of the degree of nonlinearity within complex signals

A novel method for online tracking of the changes in the non- linearity within complex-valued signals is introduced. This is achieved by a collaborative adaptive signal processing approach by means of a hybrid filter. By tracking the dynamics of the adaptive mixing parameter within the employed hybrid filtering architecture, we show that it is possible to quantify the degree of nonlinearity within complex-valued data. Simulations on both benchmark and real world data support the approach.

ONLINE DETECTION OF THE MODALITY OF COMPLEX-VALUED REAL WORLD SIGNALS

A novel method for the online detection of the modality of complex-valued nonlinear and nonstationary signals is introduced. This is achieved using a convex combination of complex nonlinear adaptive filters with different transient characteristics. To facilitate the online mode of operation, the convex mixing parameter lambda within the proposed architecture is made gradient adaptive. Our focus is on the most important aspect of complex nonlinear modeling, that is, the identification of the split-complex and fully-complex nature of the signal in hand. The algorithms derived are robust and capable of tracking the changes in the modality of both benchmark and real world radar and wind complex vector fields.

An online method for detecting nonlinearity within a signal

A novel method for online analysis of the changes in signal modality is proposed. This is achieved by tracking the dynamics of the mixing parameter within a hybrid filter rather than the actual filter performance. An implementation of the proposed hybrid filter using a combination of the Least Mean Square (LMS) and the Generalised Normalised Gradient Descent (GNGD) algorithms is analysed and the potential of such a scheme for tracking signal nonlinearity is highlighted. Simulations on linear and nonlinear signals in a prediction configuration support the analysis. Biological applications of the approach have been illustrated on EEG data of epileptic patients.

Online Detection of the Nature of Complex-Valued Signals

A novel method for on-line tracking of the changes in the nature of a complex-valued signal is proposed. This is achieved by analysing the time variation of the mixing parameter within a hybrid complex-valued nonlinear adaptive filter. The proposed hybrid filter consists of a combination of split- and fully-complex nonlinear gradient descent algorithms, whose outputs are mixed in a convex manner. A learning algorithm for this scheme is derived and the potential of such an approach for tracking of signal modality changes is highlighted. The potential of the proposed approach is supported by simulations on both a synthetic benchmark signal and on real-world radar data.

Hedging Electricity Swing Options in Incomplete Markets

The deregulation of electricity markets renders public utilities vulnerable to the high volatility of electricity spot prices. This price risk is effectively mitigated by swing options, which allow the option holder to buy electric energy from the option writer at a fixed price during a prescribed time period. Unlike many financial derivatives, a swing option cannot be assigned a unique fair value due to market frictions. In this paper we determine the options no-arbitrage price interval by hedging its payoff stream with basic market securities (such as forward contracts) both from the perspective of the holder and the writer of the option. The end points of the no-arbitrage interval are given by the optimal values of two robust control problems, which we solve in polynomial decision rules via constraint sampling.

Designing Fair, Efficient, and Interpretable Policies for Prioritizing Homeless Youth for Housing Resources

We consider the problem of designing fair, efficient, and interpretable policies for prioritizing heterogeneous homeless youth on a waiting list for scarce housing resources of different types. We focus on point-based policies that use features of the housing resources (e.g., permanent supportive housing, rapid rehousing) and the youth (e.g., age, history of substance use) to maximize the probability that the youth will have a safe and stable exit from the housing program. The policies can be used to prioritize waitlisted youth each time a housing resource is procured. Our framework provides the policy-maker the flexibility to select both their desired structure for the policy and their desired fairness requirements. Our approach can thus explicitly trade-off interpretability and efficiency while ensuring that fairness constraints are met. We propose a flexible data-driven mixed-integer optimization formulation for designing the policy, along with an approximate formulation which can be solved efficiently for broad classes of interpretable policies using Bender’s decomposition. We evaluate our framework using real-world data from the United States homeless youth housing system. We show that our framework results in policies that are more fair than the current policy in place and than classical interpretable machine learning approaches while achieving a similar (or higher) level of overall efficiency.