Risk Minimization, Regret Minimization and Progressive Hedging Algorithms

This paper begins with a study on the dual representations of risk and regret measures and their impact on modeling multistage decision making under uncertainty. A relationship between risk envelopes and regret envelopes is established by using the Lagrangian duality theory. Such a relationship opens a door to a decomposition scheme, called progressive hedging, for solving multistage risk minimization and regret minimization problems. In particular, the classical progressive hedging algorithm is modified in order to handle a new class of linkage constraints that arises from reformulations and other applications of risk and regret minimization problems. Numerical results are provided to show the efficiency of the progressive hedging algorithms.Comment: 21 pages, 2 figure

Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio

Risk-Adaptive Learning of Seismic Response using Multi-Fidelity Analysis

Performance-based earthquake engineering often requires a large number of sophisticated nonlinear time-history analyses and is therefore demanding both with regard to computing resources and technical expertise. We develop a risk-adaptive statistical learning method based on multi-fidelity analysis that enables engineers to conservatively predict structural response using only low-fidelity analyses such as Pushover analyses. Using a structural model of a 35-story building in California and a training data set consisting of nonlinear time-history and pushover analyses for 160 ground motions, we accurately and conservatively predict maximum story drift ratio, top-story drift ratio, and normalized base shear under the effect of 40 ground motions not seen during the training

Graph Neural Networks for Pressure Estimation in Water Distribution Systems

Pressure and flow estimation in Water Distribution Networks (WDN) allows water management companies to optimize their control operations. For many years, mathematical simulation tools have been the most common approach to reconstructing an estimate of the WDN hydraulics. However, pure physics-based simulations involve several challenges, e.g. partially observable data, high uncertainty, and extensive manual configuration. Thus, data-driven approaches have gained traction to overcome such limitations. In this work, we combine physics-based modeling and Graph Neural Networks (GNN), a data-driven approach, to address the pressure estimation problem. First, we propose a new data generation method using a mathematical simulation but not considering temporal patterns and including some control parameters that remain untouched in previous works; this contributes to a more diverse training data. Second, our training strategy relies on random sensor placement making our GNN-based estimation model robust to unexpected sensor location changes. Third, a realistic evaluation protocol considers real temporal patterns and additionally injects the uncertainties intrinsic to real-world scenarios. Finally, a multi-graph pre-training strategy allows the model to be reused for pressure estimation in unseen target WDNs. Our GNN-based model estimates the pressure of a large-scale WDN in The Netherlands with a MAE of 1.94mH$_2$O and a MAPE of 7%, surpassing the performance of previous studies. Likewise, it outperformed previous approaches on other WDN benchmarks, showing a reduction of absolute error up to approximately 52% in the best cases.Comment: submitted to Water Resources Research. Huy Truong and Andr\'es Tello contributed equally to this wor

Ensemble deep learning: A review

Ensemble learning combines several individual models to obtain better generalization performance. Currently, deep learning models with multilayer processing architecture is showing better performance as compared to the shallow or traditional classification models. Deep ensemble learning models combine the advantages of both the deep learning models as well as the ensemble learning such that the final model has better generalization performance. This paper reviews the state-of-art deep ensemble models and hence serves as an extensive summary for the researchers. The ensemble models are broadly categorised into ensemble models like bagging, boosting and stacking, negative correlation based deep ensemble models, explicit/implicit ensembles, homogeneous /heterogeneous ensemble, decision fusion strategies, unsupervised, semi-supervised, reinforcement learning and online/incremental, multilabel based deep ensemble models. Application of deep ensemble models in different domains is also briefly discussed. Finally, we conclude this paper with some future recommendations and research directions

Distributionally Robust Optimization: A Review

The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. This paper surveys main concepts and contributions to DRO, and its relationships with robust optimization, risk-aversion, chance-constrained optimization, and function regularization

Predictive cognition in dementia: the case of music

The clinical complexity and pathological diversity of neurodegenerative diseases impose immense challenges for diagnosis and the design of rational interventions. To address these challenges, there is a need to identify new paradigms and biomarkers that capture shared pathophysiological processes and can be applied across a range of diseases. One core paradigm of brain function is predictive coding: the processes by which the brain establishes predictions and uses them to minimise prediction errors represented as the difference between predictions and actual sensory inputs. The processes involved in processing unexpected events and responding appropriately are vulnerable in common dementias but difficult to characterise. In my PhD work, I have exploited key properties of music – its universality, ecological relevance and structural regularity – to model and assess predictive cognition in patients representing major syndromes of frontotemporal dementia – non-fluent variant PPA (nfvPPA), semantic-variant PPA (svPPA) and behavioural-variant FTD (bvFTD) - and Alzheimer’s disease relative to healthy older individuals. In my first experiment, I presented patients with well-known melodies containing no deviants or one of three types of deviant - acoustic (white-noise burst), syntactic (key-violating pitch change) or semantic (key-preserving pitch change). I assessed accuracy detecting melodic deviants and simultaneously-recorded pupillary responses to these deviants. I used voxel-based morphometry to define neuroanatomical substrates for the behavioural and autonomic processing of these different types of deviants, and identified a posterior temporo-parietal network for detection of basic acoustic deviants and a more anterior fronto-temporo-striatal network for detection of syntactic pitch deviants. In my second chapter, I investigated the ability of patients to track the statistical structure of the same musical stimuli, using a computational model of the information dynamics of music to calculate the information-content of deviants (unexpectedness) and entropy of melodies (uncertainty). I related these information-theoretic metrics to performance for detection of deviants and to ‘evoked’ and ‘integrative’ pupil reactivity to deviants and melodies respectively and found neuroanatomical correlates in bilateral dorsal and ventral striatum, hippocampus, superior temporal gyri, right temporal pole and left inferior frontal gyrus. Together, chapters 3 and 4 revealed new hypotheses about the way FTD and AD pathologies disrupt the integration of predictive errors with predictions: a retained ability of AD patients to detect deviants at all levels of the hierarchy with a preserved autonomic sensitivity to information-theoretic properties of musical stimuli; a generalized impairment of surprise detection and statistical tracking of musical information at both a cognitive and autonomic levels for svPPA patients underlying a diminished precision of predictions; the exact mirror profile of svPPA patients in nfvPPA patients with an abnormally high rate of false-alarms with up-regulated pupillary reactivity to deviants, interpreted as over-precise or inflexible predictions accompanied with normal cognitive and autonomic probabilistic tracking of information; an impaired behavioural and autonomic reactivity to unexpected events with a retained reactivity to environmental uncertainty in bvFTD patients. Chapters 5 and 6 assessed the status of reward prediction error processing and updating via actions in bvFTD. I created pleasant and aversive musical stimuli by manipulating chord progressions and used a classic reinforcement-learning paradigm which asked participants to choose the visual cue with the highest probability of obtaining a musical ‘reward’. bvFTD patients showed reduced sensitivity to the consequence of an action and lower learning rate in response to aversive stimuli compared to reward. These results correlated with neuroanatomical substrates in ventral and dorsal attention networks, dorsal striatum, parahippocampal gyrus and temporo-parietal junction. Deficits were governed by the level of environmental uncertainty with normal learning dynamics in a structured and binarized environment but exacerbated deficits in noisier environments. Impaired choice accuracy in noisy environments correlated with measures of ritualistic and compulsive behavioural changes and abnormally reduced learning dynamics correlated with behavioural changes related to empathy and theory-of-mind. Together, these experiments represent the most comprehensive attempt to date to define the way neurodegenerative pathologies disrupts the perceptual, behavioural and physiological encoding of unexpected events in predictive coding terms

Dimensionality reduction and unsupervised learning techniques applied to clinical psychiatric and neuroimaging phenotypes

Unsupervised learning and other multivariate analysis techniques are increasingly recognized in neuropsychiatric research. Here, finite mixture models and random forests were applied to clinical observations of patients with major depression to detect and validate treatment response subgroups. Further, independent component analysis and agglomerative hierarchical clustering were combined to build a brain parcellation solely on structural covariance information of magnetic resonance brain images. Übersetzte Kurzfassung: Unüberwachtes Lernen und andere multivariate Analyseverfahren werden zunehmend auf neuropsychiatrische Fragestellungen angewendet. Finite mixture Modelle wurden auf klinische Skalen von Patienten mit schwerer Depression appliziert, um Therapieantwortklassen zu bilden und mit Random Forests zu validieren. Unabhängigkeitsanalysen und agglomeratives hierarchisches Clustering wurden kombiniert, um die strukturelle Kovarianz von Magnetresonanz­tomographie-Bildern für eine Hirnparzellierung zu nutzen

Predicting the Outcome of Cognitive Training in Parkinson’s Disease using Magnetic Resonance Imaging

Motivation: Cognitive impairment is an important symptom of Parkinson’s Disease (PD), usually having a substantial negative impact on the quality of life of patients, families, and caregivers. Cognitive Training (CT) have been proven effective in halting the process of cognitive decline in PD. However, the efficacy of CT is unpredictable from subject to subject. Objective: Investigate the possibility of predicting the outcome of CT in PD patients with Mild Cognitive Impairment using structural and functional Magnetic Resonance Imaging (MRI) data. Methods: Before CT, a sample of 42 PD patients underwent structural and functional MRI. Graph measures were then extracted from their structural and functional con nectomes and used as features for random forest (RFo) and decision tree (DT) machine learning (ML) regression algorithms with and without prior latent component analysis (LCA). CT response was evaluated by assessing the outcomes of the Tower of London task pre- and post-treatment. Finally, the 4 ML models were used to predict CT response and their performances were assessed. Post hoc analyses were conducted to investigate whether these algorithms could predict age using connectomic measures on a sample of 80 PD patients. Results: The performances of the aforementioned algorithms did not differ signifi cantly from the baseline performance predicting the subject-specific CT outcome. The performance of the RFo without LCA differed significantly from the baseline performance in the age prediction task for the sample of 80 patients. Conclusion: Notwithstanding the lack of statistical significance in predicting our xicognitive outcomes, the relative success of the age prediction task points towards the potential of this approach. We hypothesise that bigger sample sizes are needed in order to predict the outcome of CT using ML