Can we identify non-stationary dynamics of trial-to-trial variability?"

Identifying sources of the apparent variability in non-stationary scenarios is a fundamental problem in many biological data analysis settings. For instance, neurophysiological responses to the same task often vary from each repetition of the same experiment (trial) to the next. The origin and functional role of this observed variability is one of the fundamental questions in neuroscience. The nature of such trial-to-trial dynamics however remains largely elusive to current data analysis approaches. A range of strategies have been proposed in modalities such as electro-encephalography but gaining a fundamental insight into latent sources of trial-to-trial variability in neural recordings is still a major challenge. In this paper, we present a proof-of-concept study to the analysis of trial-to-trial variability dynamics founded on non-autonomous dynamical systems. At this initial stage, we evaluate the capacity of a simple statistic based on the behaviour of trajectories in classification settings, the trajectory coherence, in order to identify trial-to-trial dynamics. First, we derive the conditions leading to observable changes in datasets generated by a compact dynamical system (the Duffing equation). This canonical system plays the role of a ubiquitous model of non-stationary supervised classification problems. Second, we estimate the coherence of class-trajectories in empirically reconstructed space of system states. We show how this analysis can discern variations attributable to non-autonomous deterministic processes from stochastic fluctuations. The analyses are benchmarked using simulated and two different real datasets which have been shown to exhibit attractor dynamics. As an illustrative example, we focused on the analysis of the rat's frontal cortex ensemble dynamics during a decision-making task. Results suggest that, in line with recent hypotheses, rather than internal noise, it is the deterministic trend which most likely underlies the observed trial-to-trial variability. Thus, the empirical tool developed within this study potentially allows us to infer the source of variability in in-vivo neural recordings

Continual learning from stationary and non-stationary data

Continual learning aims at developing models that are capable of working on constantly evolving problems over a long-time horizon. In such environments, we can distinguish three essential aspects of training and maintaining machine learning models - incorporating new knowledge, retaining it and reacting to changes. Each of them poses its own challenges, constituting a compound problem with multiple goals. Remembering previously incorporated concepts is the main property of a model that is required when dealing with stationary distributions. In non-stationary environments, models should be capable of selectively forgetting outdated decision boundaries and adapting to new concepts. Finally, a significant difficulty can be found in combining these two abilities within a single learning algorithm, since, in such scenarios, we have to balance remembering and forgetting instead of focusing only on one aspect. The presented dissertation addressed these problems in an exploratory way. Its main goal was to grasp the continual learning paradigm as a whole, analyze its different branches and tackle identified issues covering various aspects of learning from sequentially incoming data. By doing so, this work not only filled several gaps in the current continual learning research but also emphasized the complexity and diversity of challenges existing in this domain. Comprehensive experiments conducted for all of the presented contributions have demonstrated their effectiveness and substantiated the validity of the stated claims

Adaptive Algorithms For Classification On High-Frequency Data Streams: Application To Finance

Mención Internacional en el título de doctorIn recent years, the problem of concept drift has gained importance in the financial domain. The succession of manias, panics and crashes have stressed the nonstationary nature and the likelihood of drastic structural changes in financial markets. The most recent literature suggests the use of conventional machine learning and statistical approaches for this. However, these techniques are unable or slow to adapt to non-stationarities and may require re-training over time, which is computationally expensive and brings financial risks. This thesis proposes a set of adaptive algorithms to deal with high-frequency data streams and applies these to the financial domain. We present approaches to handle different types of concept drifts and perform predictions using up-to-date models. These mechanisms are designed to provide fast reaction times and are thus applicable to high-frequency data. The core experiments of this thesis are based on the prediction of the price movement direction at different intraday resolutions in the SPDR S&P 500 exchange-traded fund. The proposed algorithms are benchmarked against other popular methods from the data stream mining literature and achieve competitive results. We believe that this thesis opens good research prospects for financial forecasting during market instability and structural breaks. Results have shown that our proposed methods can improve prediction accuracy in many of these scenarios. Indeed, the results obtained are compatible with ideas against the efficient market hypothesis. However, we cannot claim that we can beat consistently buy and hold; therefore, we cannot reject it.Programa de Doctorado en Ciencia y Tecnología Informática por la Universidad Carlos III de MadridPresidente: Gustavo Recio Isasi.- Secretario: Pedro Isasi Viñuela.- Vocal: Sandra García Rodrígue

New perspectives and methods for stream learning in the presence of concept drift.

153 p.Applications that generate data in the form of fast streams from non-stationary environments, that is,those where the underlying phenomena change over time, are becoming increasingly prevalent. In thiskind of environments the probability density function of the data-generating process may change overtime, producing a drift. This causes that predictive models trained over these stream data become obsoleteand do not adapt suitably to the new distribution. Specially in online learning scenarios, there is apressing need for new algorithms that adapt to this change as fast as possible, while maintaining goodperformance scores. Examples of these applications include making inferences or predictions based onfinancial data, energy demand and climate data analysis, web usage or sensor network monitoring, andmalware/spam detection, among many others.Online learning and concept drift are two of the most hot topics in the recent literature due to theirrelevance for the so-called Big Data paradigm, where nowadays we can find an increasing number ofapplications based on training data continuously available, named as data streams. Thus, learning in nonstationaryenvironments requires adaptive or evolving approaches that can monitor and track theunderlying changes, and adapt a model to accommodate those changes accordingly. In this effort, Iprovide in this thesis a comprehensive state-of-the-art approaches as well as I identify the most relevantopen challenges in the literature, while focusing on addressing three of them by providing innovativeperspectives and methods.This thesis provides with a complete overview of several related fields, and tackles several openchallenges that have been identified in the very recent state of the art. Concretely, it presents aninnovative way to generate artificial diversity in ensembles, a set of necessary adaptations andimprovements for spiking neural networks in order to be used in online learning scenarios, and finally, adrift detector based on this former algorithm. All of these approaches together constitute an innovativework aimed at presenting new perspectives and methods for the field

New perspectives and methods for stream learning in the presence of concept drift.

153 p.Applications that generate data in the form of fast streams from non-stationary environments, that is,those where the underlying phenomena change over time, are becoming increasingly prevalent. In thiskind of environments the probability density function of the data-generating process may change overtime, producing a drift. This causes that predictive models trained over these stream data become obsoleteand do not adapt suitably to the new distribution. Specially in online learning scenarios, there is apressing need for new algorithms that adapt to this change as fast as possible, while maintaining goodperformance scores. Examples of these applications include making inferences or predictions based onfinancial data, energy demand and climate data analysis, web usage or sensor network monitoring, andmalware/spam detection, among many others.Online learning and concept drift are two of the most hot topics in the recent literature due to theirrelevance for the so-called Big Data paradigm, where nowadays we can find an increasing number ofapplications based on training data continuously available, named as data streams. Thus, learning in nonstationaryenvironments requires adaptive or evolving approaches that can monitor and track theunderlying changes, and adapt a model to accommodate those changes accordingly. In this effort, Iprovide in this thesis a comprehensive state-of-the-art approaches as well as I identify the most relevantopen challenges in the literature, while focusing on addressing three of them by providing innovativeperspectives and methods.This thesis provides with a complete overview of several related fields, and tackles several openchallenges that have been identified in the very recent state of the art. Concretely, it presents aninnovative way to generate artificial diversity in ensembles, a set of necessary adaptations andimprovements for spiking neural networks in order to be used in online learning scenarios, and finally, adrift detector based on this former algorithm. All of these approaches together constitute an innovativework aimed at presenting new perspectives and methods for the field