We consider inference problems for a class of continuous state collective hidden Markov models, where the data is recorded in aggregate (collective) form generated by a large population of individuals following the same dynamics. We propose an aggregate inference algorithm called collective Gaussian forward-backward algorithm, extending recently proposed Sinkhorn belief propagation algorithm to models characterized by Gaussian densities. Our algorithm enjoys convergence guarantee. In addition, it reduces to the standard Kalman filter when the observations are generated by a single individual. The efficacy of the proposed algorithm is demonstrated through multiple experiments.

Machine learning models always make a prediction, even when it is likely to be inaccurate. This behavior should be avoided in many decision support applications, where mistakes can have severe consequences. Albeit already studied in 1970, machine learning with a reject option recently gained interest. This machine learning subfield enables machine learning models to abstain from making a prediction when likely to make a mistake. This survey aims to provide an overview on machine learning with a reject option. We introduce the conditions leading to two types of rejection, ambiguity and novelty rejection. Moreover, we define the existing architectures for models with a reject option, describe the standard learning strategies to train such models and relate traditional machine learning techniques to rejection. Additionally, we review strategies to evaluate a model's predictive and rejective quality. Finally, we provide examples of relevant application domains and show how machine learning with rejection relates to other machine learning research areas.

Objective: Temporal electronic health records (EHRs) can be a wealth of information for secondary uses, such as clinical events prediction or chronic disease management. However, challenges exist for temporal data representation. We therefore sought to identify these challenges and evaluate novel methodologies for addressing them through a systematic examination of deep learning solutions. Methods: We searched five databases (PubMed, EMBASE, the Institute of Electrical and Electronics Engineers [IEEE] Xplore Digital Library, the Association for Computing Machinery [ACM] digital library, and Web of Science) complemented with hand-searching in several prestigious computer science conference proceedings. We sought articles that reported deep learning methodologies on temporal data representation in structured EHR data from January 1, 2010, to August 30, 2020. We summarized and analyzed the selected articles from three perspectives: nature of time series, methodology, and model implementation. Results: We included 98 articles related to temporal data representation using deep learning. Four major challenges were identified, including data irregularity, data heterogeneity, data sparsity, and model opacity. We then studied how deep learning techniques were applied to address these challenges. Finally, we discuss some open challenges arising from deep learning. Conclusion: Temporal EHR data present several major challenges for clinical prediction modeling and data utilization. To some extent, current deep learning solutions can address these challenges. Future studies can consider designing comprehensive and integrated solutions. Moreover, researchers should incorporate additional clinical domain knowledge into study designs and enhance the interpretability of the model to facilitate its implementation in clinical practice.

Many transfer problems require re-using previously optimal decisions for solving new tasks, which suggests the need for learning algorithms that can modify the mechanisms for choosing certain actions independently of those for choosing others. However, there is currently no formalism nor theory for how to achieve this kind of modular credit assignment. To answer this question, we define modular credit assignment as a constraint on minimizing the algorithmic mutual information among feedback signals for different decisions. We introduce what we call the modularity criterion for testing whether a learning algorithm satisfies this constraint by performing causal analysis on the algorithm itself. We generalize the recently proposed societal decision-making framework as a more granular formalism than the Markov decision process to prove that for decision sequences that do not contain cycles, certain single-step temporal difference action-value methods meet this criterion while all policy-gradient methods do not. Empirical evidence suggests that such action-value methods are more sample efficient than policy-gradient methods on transfer problems that require only sparse changes to a sequence of previously optimal decisions.

Markov Decision Processes (MDPs) are an effective way to formally describe many Machine Learning problems. In fact, recently MDPs have also emerged as a powerful framework to model financial trading tasks. For example, financial MDPs can model different market scenarios. However, the learning of a (near-)optimal policy for each of these financial MDPs can be a very time-consuming process, especially when nothing is known about the policy to begin with. An alternative approach is to find a similar financial MDP for which we have already learned its policy, and then reuse such policy in the learning of a new policy for a new financial MDP. Such a knowledge transfer between market scenarios raises several issues. On the one hand, how to measure the similarity between financial MDPs. On the other hand, how to use this similarity measurement to effectively transfer the knowledge between financial MDPs. This paper addresses both of these issues. Regarding the first one, this paper analyzes the use of three similarity metrics based on conceptual, structural and performance aspects of the financial MDPs. Regarding the second one, this paper uses Probabilistic Policy Reuse to balance the exploitation/exploration in the learning of a new financial MDP according to the similarity of the previous financial MDPs whose knowledge is reused.

We consider a general statistical estimation problem wherein binary labels across different observations are not independent conditioned on their feature vectors, but dependent, capturing settings where e.g. these observations are collected on a spatial domain, a temporal domain, or a social network, which induce dependencies. We model these dependencies in the language of Markov Random Fields and, importantly, allow these dependencies to be substantial, i.e do not assume that the Markov Random Field capturing these dependencies is in high temperature. As our main contribution we provide algorithms and statistically efficient estimation rates for this model, giving several instantiations of our bounds in logistic regression, sparse logistic regression, and neural network settings with dependent data. Our estimation guarantees follow from novel results for estimating the parameters (i.e. external fields and interaction strengths) of Ising models from a {\em single} sample. {We evaluate our estimation approach on real networked data, showing that it outperforms standard regression approaches that ignore dependencies, across three text classification datasets: Cora, Citeseer and Pubmed.}

Reward-Weighted Regression (RWR) belongs to a family of widely known iterative Reinforcement Learning algorithms based on the Expectation-Maximization framework. In this family, learning at each iteration consists of sampling a batch of trajectories using the current policy and fitting a new policy to maximize a return-weighted log-likelihood of actions. Although RWR is known to yield monotonic improvement of the policy under certain circumstances, whether and under which conditions RWR converges to the optimal policy have remained open questions. In this paper, we provide for the first time a proof that RWR converges to a global optimum when no function approximation is used.

Stochastic gradient Markov chain Monte Carlo (SGMCMC) is considered the gold standard for Bayesian inference in large-scale models, such as Bayesian neural networks. Since practitioners face speed versus accuracy tradeoffs in these models, variational inference (VI) is often the preferable option. Unfortunately, VI makes strong assumptions on both the factorization and functional form of the posterior. In this work, we propose a new non-parametric variational approximation that makes no assumptions about the approximate posterior's functional form and allows practitioners to specify the exact dependencies the algorithm should respect or break. The approach relies on a new Langevin-type algorithm that operates on a modified energy function, where parts of the latent variables are averaged over samples from earlier iterations of the Markov chain. This way, statistical dependencies can be broken in a controlled way, allowing the chain to mix faster. This scheme can be further modified in a ''dropout'' manner, leading to even more scalability. By implementing the scheme on a ResNet-20 architecture, we obtain better predictive likelihoods and larger effective sample sizes than full SGMCMC.

Time series of data arising across geophysical sciences, remote sensing, automatic control, and a variety of other scientific and engineering applications often reflect observations of an underlying dynamical system operating in a latent state-space. Estimating the evolution of this latent state from data is the central challenge of data assimilation (DA) [28, 39, 49, 68, 75]. However, in these and other applications, we often lack an accurate model of the underlying dynamics, and the dynamical model needs to be learned from the observations to perform DA. This paper introduces auto-differentiable ensemble Kalman filters (AD-EnKFs), a machine learning (ML) framework for the principled co-learning of states and dynamics. This framework enables learning in three core categories of unknown dynamics: (a) parametric dynamical models with unknown parameter values; (b) fully-unknown dynamics captured using neural network (NN) surrogate models; and (c) inaccurate or partially-known dynamical models that can be improved using NN corrections. AD-EnKFs are designed to scale to high-dimensional states, observations, and NN surrogate models. In order to describe the main idea behind the AD-EnKF framework, let us introduce briefly the problem of interest. Our setting will be formalized in §2 below.

AI in finance broadly refers to the applications of AI techniques in financial businesses. This area has been lasting for decades with both classic and modern AI techniques applied to increasingly broader areas of finance, economy and society. In contrast to either discussing the problems, aspects and opportunities of finance that have benefited from specific AI techniques and in particular some new-generation AI and data science (AIDS) areas or reviewing the progress of applying specific techniques to resolving certain financial problems, this review offers a comprehensive and dense roadmap of the overwhelming challenges, techniques and opportunities of AI research in finance over the past decades. The landscapes and challenges of financial businesses and data are firstly outlined, followed by a comprehensive categorization and a dense overview of the decades of AI research in finance. We then structure and illustrate the data-driven analytics and learning of financial businesses and data. The comparison, criticism and discussion of classic vs. modern AI techniques for finance are followed. Lastly, open issues and opportunities address future AI-empowered finance and finance-motivated AI research.