High-Dimensional Prediction for Sequential Decision Making

We study the problem of making predictions of an adversarially chosen high-dimensional state that are unbiased subject to an arbitrary collection of conditioning events, with the goal of tailoring these events to downstream decision makers. We give efficient algorithms for solving this problem, as well as a number of applications that stem from choosing an appropriate set of conditioning events. For example, we can efficiently make predictions targeted at polynomially many decision makers, giving each of them optimal swap regret if they best-respond to our predictions. We generalize this to online combinatorial optimization, where the decision makers have a very large action space, to give the first algorithms offering polynomially many decision makers no regret on polynomially many subsequences that may depend on their actions and the context. We apply these results to get efficient no-subsequence-regret algorithms in extensive-form games (EFGs), yielding a new family of regret guarantees for EFGs that generalizes some existing EFG regret notions, e.g. regret to informed causal deviations, and is generally incomparable to other known such notions. Next, we develop a novel transparent alternative to conformal prediction for building valid online adversarial multiclass prediction sets. We produce class scores that downstream algorithms can use for producing valid-coverage prediction sets, as if these scores were the true conditional class probabilities. We show this implies strong conditional validity guarantees including set-size-conditional and multigroup-fair coverage for polynomially many downstream prediction sets. Moreover, our class scores can be guaranteed to have improved $L_2$ loss, cross-entropy loss, and generally any Bregman loss, compared to any collection of benchmark models, yielding a high-dimensional real-valued version of omniprediction.Comment: Added references, Arxiv abstract edite

Accelerating inference in cosmology and seismology with generative models

Statistical analyses in many physical sciences require running simulations of the system that is being examined. Such simulations provide complementary information to the theoretical analytic models, and represent an invaluable tool to investigate the dynamics of complex systems. However, running simulations is often computationally expensive, and the high number of required mocks to obtain sufficient statistical precision often makes the problem intractable. In recent years, machine learning has emerged as a possible solution to speed up the generation of scientific simulations. Machine learning generative models usually rely on iteratively feeding some true simulations to the algorithm, until it learns the important common features and is capable of producing accurate simulations in a fraction of the time. In this thesis, advanced machine learning algorithms are explored and applied to the challenge of accelerating physical simulations. Various techniques are applied to problems in cosmology and seismology, showing benefits and limitations of such an approach through a critical analysis. The algorithms are applied to compelling problems in the fields, including surrogate models for the seismic wave equation, the emulation of cosmological summary statistics, and the fast generation of large simulations of the Universe. These problems are formulated within a relevant statistical framework, and tied to real data analysis pipelines. In the conclusions, a critical overview of the results is provided, together with an outlook over possible future expansions of the work presented in the thesis

Beyond Statistical Fairness

In recent years, a great deal of fairness notions has been proposed. Yet, most of them take a reductionist approach by indirectly viewing fairness as equalizing some error statistic across pre-defined groups. This thesis aims to explore some ideas as to how to go beyond such statistical fairness frameworks. First, we consider settings in which the right notion of fairness may not be captured by simple mathematical definitions but might be more complex and nuanced and thus require elicitation from individual or collective stakeholders. By asking stakeholders to make pairwise comparisons to learn which pair of individuals should be treated similarly, we show how to approximately learn the most accurate classifier or converge to such one subject to the elicited fairness constraints. We consider an offline setting where the pairwise comparisons must be made prior to training a model and an online setting where one can continually provide fairness feedback to the deployed model in each round. We also report preliminary findings of a behavioral study of our framework using human-subject fairness constraints elicited on the COMPAS criminal recidivism dataset. Second, unlike most of the statistical fairness framework that promises fairness for pre-defined and often coarse groups, we provide fairness guarantees for finer subgroups, such as all possible intersections of the pre-defined groups, in the context of uncertainty estimation in both offline and online setting. Our framework gives uncertainty guarantees that are more locally sensible than the ones given by conformal prediction techniques; our uncertainty estimates are valid even when averaged over any subgroup, but uncertainty estimates in conformal predictions are usually only valid when averaged over the entire population

Neural-Kalman Schemes for Non-Stationary Channel Tracking and Learning

This Thesis focuses on channel tracking in Orthogonal Frequency-Division Multiplexing (OFDM), a widely-used method of data transmission in wireless communications, when abrupt changes occur in the channel. In highly mobile applications, new dynamics appear that might make channel tracking non-stationary, e.g. channels might vary with location, and location rapidly varies with time. Simple examples might be the di erent channel dynamics a train receiver faces when it is close to a station vs. crossing a bridge vs. entering a tunnel, or a car receiver in a route that grows more tra c-dense. Some of these dynamics can be modelled as channel taps dying or being reborn, and so tap birth-death detection is of the essence. In order to improve the quality of communications, we delved into mathematical methods to detect such abrupt changes in the channel, such as the mathematical areas of Sequential Analysis/ Abrupt Change Detection and Random Set Theory (RST), as well as the engineering advances in Neural Network schemes. This knowledge helped us nd a solution to the problem of abrupt change detection by informing and inspiring the creation of low-complexity implementations for real-world channel tracking. In particular, two such novel trackers were created: the Simpli- ed Maximum A Posteriori (SMAP) and the Neural-Network-switched Kalman Filtering (NNKF) schemes. The SMAP is a computationally inexpensive, threshold-based abrupt-change detector. It applies the three following heuristics for tap birth-death detection: a) detect death if the tap gain jumps into approximately zero (memoryless detection); b) detect death if the tap gain has slowly converged into approximately zero (memory detection); c) detect birth if the tap gain is far from zero. The precise parameters for these three simple rules can be approximated with simple theoretical derivations and then ne-tuned through extensive simulations. The status detector for each tap using only these three computationally inexpensive threshold comparisons achieves an error reduction matching that of a close-to-perfect path death/birth detection, as shown in simulations. This estimator was shown to greatly reduce channel tracking error in the target Signal-to-Noise Ratio (SNR) range at a very small computational cost, thus outperforming previously known systems. The underlying RST framework for the SMAP was then extended to combined death/birth and SNR detection when SNR is dynamical and may drift. We analyzed how di erent quasi-ideal SNR detectors a ect the SMAP-enhanced Kalman tracker's performance. Simulations showed SMAP is robust to SNR drift in simulations, although it was also shown to bene t from an accurate SNR detection. The core idea behind the second novel tracker, NNKFs, is similar to the SMAP, but now the tap birth/death detection will be performed via an arti cial neuronal network (NN). Simulations show that the proposed NNKF estimator provides extremely good performance, practically identical to a detector with 100% accuracy. These proposed Neural-Kalman schemes can work as novel trackers for multipath channels, since they are robust to wide variations in the probabilities of tap birth and death. Such robustness suggests a single, low-complexity NNKF could be reusable over di erent tap indices and communication environments. Furthermore, a di erent kind of abrupt change was proposed and analyzed: energy shifts from one channel tap to adjacent taps (partial tap lateral hops). This Thesis also discusses how to model, detect and track such changes, providing a geometric justi cation for this and additional non-stationary dynamics in vehicular situations, such as road scenarios where re ections on trucks and vans are involved, or the visual appearance/disappearance of drone swarms. An extensive literature review of empirically-backed abrupt-change dynamics in channel modelling/measuring campaigns is included. For this generalized framework of abrupt channel changes that includes partial tap lateral hopping, a neural detector for lateral hops with large energy transfers is introduced. Simulation results suggest the proposed NN architecture might be a feasible lateral hop detector, suitable for integration in NNKF schemes. Finally, the newly found understanding of abrupt changes and the interactions between Kalman lters and neural networks is leveraged to analyze the neural consequences of abrupt changes and brie y sketch a novel, abrupt-change-derived stochastic model for neural intelligence, extract some neuro nancial consequences of unstereotyped abrupt dynamics, and propose a new portfolio-building mechanism in nance: Highly Leveraged Abrupt Bets Against Failing Experts (HLABAFEOs). Some communication-engineering-relevant topics, such as a Bayesian stochastic stereotyper for hopping Linear Gauss-Markov (LGM) models, are discussed in the process. The forecasting problem in the presence of expert disagreements is illustrated with a hopping LGM model and a novel structure for a Bayesian stereotyper is introduced that might eventually solve such problems through bio-inspired, neuroscienti cally-backed mechanisms, like dreaming and surprise (biological Neural-Kalman). A generalized framework for abrupt changes and expert disagreements was introduced with the novel concept of Neural-Kalman Phenomena. This Thesis suggests mathematical (Neural-Kalman Problem Category Conjecture), neuro-evolutionary and social reasons why Neural-Kalman Phenomena might exist and found signi cant evidence for their existence in the areas of neuroscience and nance. Apart from providing speci c examples, practical guidelines and historical (out)performance for some HLABAFEO investing portfolios, this multidisciplinary research suggests that a Neural- Kalman architecture for ever granular stereotyping providing a practical solution for continual learning in the presence of unstereotyped abrupt dynamics would be extremely useful in communications and other continual learning tasks.Programa de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Luis Castedo Ribas.- Secretaria: Ana García Armada.- Vocal: José Antonio Portilla Figuera