Understanding local currents in the North Atlantic region of the ocean is a key part of modelling heat transfer and global climate patterns. Satellites provide a surface signature of the temperature of the ocean with a high horizontal resolution while in situ autonomous probes supply high vertical resolution, but horizontally sparse, knowledge of the ocean interior thermal structure. The objective of this paper is to develop a methodology to combine these complementary ocean observing systems measurements to obtain a three-dimensional time series of ocean temperatures with high horizontal and vertical resolution. Within an observation-driven framework, we investigate the extent to which mesoscale ocean dynamics in the North Atlantic region may be decomposed into a mixture of dynamical modes, characterized by different local regressions between Sea Surface Temperature (SST), Sea Level Anomalies (SLA) and Vertical Temperature fields. Ultimately we propose a Latent-class regression method to improve prediction of vertical ocean temperature.

Adversarial Regression is a proposition to perform high dimensional non-linear regression with uncertainty estimation. We used Conditional Generative Adversarial Network to obtain an estimate of the full predictive distribution for a new observation. Generative Adversarial Networks (GAN) are implicit generative models which produce samples from a distribution approximating the distribution of the data. The conditional version of it (CGAN) takes the following expression: $\min\limits_G \max\limits_D V(D, G) = \mathbb{E}_{x\sim p_{r}(x)} [log(D(x, y))] + \mathbb{E}_{z\sim p_{z}(z)} [log (1-D(G(z, y)))]$. An approximate solution can be found by training simultaneously two neural networks to model D and G and feeding G with a random noise vector $z$. After training, we have that $G(z, y)\mathrel{\dot\sim} p_{data}(x, y)$. By fixing $y$, we have $G(z|y) \mathrel{\dot\sim} p{data}(x|y)$. By sampling $z$, we can therefore obtain samples following approximately $p(x|y)$, which is the predictive distribution of $x$ for a new $y$. We ran experiments to test various loss functions, data distributions, sample size, size of the noise vector, etc. Even if we observed differences, no experiment outperformed consistently the others. The quality of CGAN for regression relies on fine-tuning a range of hyperparameters. In a broader view, the results show that CGANs are very promising methods to perform uncertainty estimation for high dimensional non-linear regression.

Learning causal graphical models based on directed acyclic graphs is an important task in causal discovery and causal inference. We consider a general framework towards efficient causal structure learning with potentially large graphs. Within this framework, we propose a masked gradient-based structure learning method based on binary adjacency matrix that exists for any structural equation model. To enable first-order optimization methods, we use Gumbel-Softmax approach to approximate the binary valued entries of the adjacency matrix, which usually results in real values that are close to zero or one. The proposed method can readily include any differentiable score function and model function for learning causal structures. Experiments on both synthetic and real-world datasets are conducted to show the effectiveness of our approach.

In clinical research, the lack of events of interest often necessitates imbalanced learning. One approach to resolve this obstacle is data integration or sharing, but due to privacy concerns neither is practical. Therefore, there is an increasing demand for a platform on which an analysis can be performed in a federated environment while maintaining privacy. However, it is quite challenging to develop a federated learning algorithm that can address both privacy-preserving and class imbalanced issues. In this study, we introduce a federated generative model learning platform for generating samples in a data-distributed environment while preserving privacy. We specifically propose approximate Bayesian computation-based Gaussian Mixture Model called 'Federated ABC-GMM', which can oversample data in a minor class by estimating the posterior distribution of model parameters across institutions in a privacy-preserving manner. PhysioNet2012, a dataset for prediction of mortality of patients in an Intensive Care Unit (ICU), was used to verify the performance of the proposed method. Experimental results show that our method boosts classification performance in terms of F1 score up to nearly an ideal situation. It is believed that the proposed method can be a novel alternative to solving class imbalance problems.

We consider a setting in which the objective is to learn to navigate in a controlled Markov process (CMP) where transition probabilities may abruptly change. For this setting, we propose a performance measure called exploration steps which counts the time steps at which the learner lacks sufficient knowledge to navigate its environment efficiently. We devise a learning meta-algorithm, MNM, and prove an upper bound on the exploration steps in terms of the number of changes.

Artificial neural networks have exceeded human-level performance in accomplishing several individual tasks (e.g. voice recognition, object recognition, and video games). However, such success remains modest compared to human intelligence that can learn and perform an unlimited number of tasks. Humans' ability of learning and accumulating knowledge over their lifetime is an essential aspect of their intelligence. Continual machine learning aims at a higher level of machine intelligence through providing the artificial agents with the ability to learn online from a non-stationary and never-ending stream of data. A key component of such a never-ending learning process is to overcome the catastrophic forgetting of previously seen data, a problem that neural networks are well known to suffer from. The work described in this thesis has been dedicated to the investigation of continual learning and solutions to mitigate the forgetting phenomena in neural networks. To approach the continual learning problem, we first assume a task incremental setting where tasks are received one at a time and data from previous tasks are not stored. Since the task incremental setting can't be assumed in all continual learning scenarios, we also study the more general online continual setting. We consider an infinite stream of data drawn from a non-stationary distribution with a supervisory or self-supervisory training signal. The proposed methods in this thesis have tackled important aspects of continual learning. They were evaluated on different benchmarks and over various learning sequences. Advances in the state of the art of continual learning have been shown and challenges for bringing continual learning into application were critically identified.

Decisions in public health are almost always made in the context of uncertainty. Policy makers responsible for making important decisions are faced with the daunting task of choosing from many possible options. This task is called planning under uncertainty, and is particularly acute when addressing complex systems, such as issues of global health and development. Decision making under uncertainty is a challenging task, and all too often this uncertainty is averaged away to simplify results for policy makers. A popular way to approach this task is to formulate the problem at hand as a (partially observable) Markov decision process, (PO)MDP. This work aims to apply these AI efforts to challenging problems in health and development. In this paper, we developed a framework for optimal health policy design in a dynamic setting. We apply a stochastic dynamic programing approach to identify both the optimal time to change the health intervention policy and the optimal time to collect decision relevant information.

Critical infrastructure systems such as electric power networks, water networks, and transportation systems play a major role in the welfare of any community. In the aftermath of disasters, their recovery is of paramount importance; orderly and efficient recovery involves the assignment of limited resources (a combination of human repair workers and machines) to repair damaged infrastructure components. The decision maker must also deal with uncertainty in the outcome of the resource-allocation actions during recovery. The manual assignment of resources seldom is optimal despite the expertise of the decision maker because of the large number of choices and uncertainties in consequences of sequential decisions. This combinatorial assignment problem under uncertainty is known to be \mbox{NP-hard}. We propose a novel decision technique that addresses the massive number of decision choices for large-scale real-world problems; in addition, our method also features an experiential learning component that adaptively determines the utilization of the computational resources based on the performance of a small number of choices. Our framework is closed-loop, and naturally incorporates all the attractive features of such a decision-making system. In contrast to myopic approaches, which do not account for the future effects of the current choices, our methodology has an anticipatory learning component that effectively incorporates \emph{lookahead} into the solutions. To this end, we leverage the theory of regression analysis, Markov decision processes (MDPs), multi-armed bandits, and stochastic models of community damage from natural disasters to develop a method for near-optimal recovery of communities. Our method contributes to the general problem of MDPs with massive action spaces with application to recovery of communities affected by hazards.

This post assumes you have some basic knowledge of probability and statistics. If you don't, do not be afraid, I have gathered a list of the best resources I could find to introduce you to these subjects, so that you can read this post, understand it, and enjoy it to its fullest. In it, we will talk about one of the most famous and utilised theorems of probability theory: Bayes' Theorem. Then you are in for a treat! Know what it is already?

Information theory is a subfield of mathematics concerned with transmitting data across a noisy channel. A cornerstone of information theory is the idea of quantifying how much information there is in a message. More generally, this can be used to quantify the information in an event and a random variable, called entropy, and is calculated using probability. Calculating information and entropy is a useful tool in machine learning and is used as the basis for techniques such as feature selection, building decision trees, and, more generally, fitting classification models. As such, a machine learning practitioner requires a strong understanding and intuition for information and entropy.