Often, mathematical models of the real world are simplified representations of complex systems. A caveat to using models for analysis is that predicted causal effects and conditional independences may not be robust under model extensions, and therefore applicability of such models is limited. In this work, we consider conditions under which qualitative model predictions are preserved when two models are combined. We show how to use the technique of causal ordering to efficiently assess the robustness of qualitative model predictions and characterize a large class of model extensions that preserve these predictions. For dynamical systems at equilibrium, we demonstrate how novel insights help to select appropriate model extensions and to reason about the presence of feedback loops. We apply our ideas to a viral infection model with immune responses.

This paper considers parameter estimation for nonlinear state-space models, which is an important but challenging problem. We address this challenge by employing a variational inference (VI) approach, which is a principled method that has deep connections to maximum likelihood estimation. This VI approach ultimately provides estimates of the model as solutions to an optimisation problem, which is deterministic, tractable and can be solved using standard optimisation tools. A specialisation of this approach for systems with additive Gaussian noise is also detailed. The proposed method is examined numerically on a range of simulation and real examples with a focus on robustness to parameter initialisations; we additionally perform favourable comparisons against state-of-the-art alternatives.

We present a model for Bayesian filtering (BF) in discrete dynamic systems where multiple entities (inter)-act, i.e. where the system dynamics is naturally described by a Multiset rewriting system (MRS). Typically, BF in such situations is computationally expensive due to the high number of discrete states that need to be maintained explicitly. We devise a lifted state representation, based on a suitable decomposition of multiset states, such that some factors of the distribution are exchangeable and thus afford an efficient representation. Intuitively, this representation groups together similar entities whose properties follow an exchangeable joint distribution. Subsequently, we introduce a BF algorithm that works directly on lifted states, without resorting to the original, much larger ground representation. This algorithm directly lends itself to approximate versions by limiting the number of explicitly represented lifted states in the posterior. We show empirically that the lifted representation can lead to a factorial reduction in the representational complexity of the distribution, and in the approximate cases can lead to a lower variance of the estimate and a lower estimation error compared to the original, ground representation.

Thompson sampling (TS) has emerged as a robust technique for contextual bandit problems. However, TS requires posterior inference and optimization for action generation, prohibiting its use in many internet applications where latency and ease of deployment are of concern. We propose a novel imitation-learning-based algorithm that distills a TS policy into an explicit policy representation by performing posterior inference and optimization offline. The explicit policy representation enables fast online decision-making and easy deployment in mobile and server-based environments. Our algorithm iteratively performs offline batch updates to the TS policy and learns a new imitation policy. Since we update the TS policy with observations collected under the imitation policy, our algorithm emulates an off-policy version of TS. Our imitation algorithm guarantees Bayes regret comparable to TS, up to the sum of single-step imitation errors. We show these imitation errors can be made arbitrarily small when unlabeled contexts are cheaply available, which is the case for most large-scale internet applications. Empirically, we show that our imitation policy achieves comparable regret to TS, while reducing decision-time latency by over an order of magnitude.

We develop data-driven methods for incorporating physical information for priors to learn parsimonious representations of nonlinear systems arising from parameterized PDEs and mechanics. Our approach is based on Variational Autoencoders (VAEs) for learning from observations nonlinear state space models. We develop ways to incorporate geometric and topological priors through general manifold latent space representations. We investigate the performance of our methods for learning low dimensional representations for the nonlinear Burgers equation and constrained mechanical systems.

Many practical machine learning tasks can be framed as Structured prediction problems, where several output variables are predicted and considered interdependent. Recent theoretical advances in structured prediction have focused on obtaining fast rates convergence guarantees, especially in the Implicit Loss Embedding (ILE) framework. PAC-Bayes has gained interest recently for its capacity of producing tight risk bounds for predictor distributions. This work proposes a novel PAC-Bayes perspective on the ILE Structured prediction framework. We present two generalization bounds, on the risk and excess risk, which yield insights into the behavior of ILE predictors. Two learning algorithms are derived from these bounds.

One way to understand how the brain adapts to its environment is to view it as a type of generative pattern-creation model [20], one that is engaged in a never-ending process of self-correction, often without external teaching signals (or labels) [53]. Under this perspective, the brain is continuously making predictions about elements of its environment, a process that allows it to infer useful representations of the sensory data it receives [56] as well as to synthesize novel patterns, which could serve as the potential basis for long-term planning and imagination itself [12]. From the theoretical viewpoint of predictive processing, the brain could be likened to a hierarchical model whose levels are implemented by neurons (or clusters of neurons). If levels are likened to regions of the brain, the neurons at one level (region) attempt to predict the state of neurons at another level (region) and adjust/correct their local model synaptic parameters based on how different their predictions were from the observed signal. Furthermore, these neurons utilize various mechanisms to laterally stimulate/suppress each other [40] to facilitate contextual processing (such as grouping/segmenting visual components of objects in a scene).

Albeit worryingly underrated in the recent literature on machine learning in general (and, on deep learning in particular), multivariate density estimation is a fundamental task in many applications, at least implicitly, and still an open issue. With a few exceptions, deep neural networks (DNNs) have seldom been applied to density estimation, mostly due to the unsupervised nature of the estimation task, and (especially) due to the need for constrained training algorithms that ended up realizing proper probabilistic models that satisfy Kolmogorov's axioms. Moreover, in spite of the well-known improvement in terms of modeling capabilities yielded by mixture models over plain single-density statistical estimators, no proper mixtures of multivariate DNN-based component densities have been investigated so far. The paper fills this gap by extending our previous work on Neural Mixture Densities (NMMs) to multivariate DNN mixtures. A maximum-likelihood (ML) algorithm for estimating Deep NMMs (DNMMs) is handed out, which satisfies numerically a combination of hard and soft constraints aimed at ensuring satisfaction of Kolmogorov's axioms. The class of probability density functions that can be modeled to any degree of precision via DNMMs is formally defined. A procedure for the automatic selection of the DNMM architecture, as well as of the hyperparameters for its ML training algorithm, is presented (exploiting the probabilistic nature of the DNMM). Experimental results on univariate and multivariate data are reported on, corroborating the effectiveness of the approach and its superiority to the most popular statistical estimation techniques.

"Computers are able to see, hear and learn. The biggest advancement that software technology has achieved in the last decade has to be the concept of artificial intelligence. Today, we encounter the perks of artificial intelligence at almost every step in our day-to-day life and also, in professional scenario. As per research, $28.5 billion has been already allocated to artificial intelligence worldwide during the first quarter of 2019. The monetary and human investment in artificial intelligence proves that it forms a core part of future technologies.

Social media popularity and importance is on the increase, due to people using it for various types of social interaction across multiple channels. This social interaction by online users includes submission of feedback, opinions and recommendations about various individuals, entities, topics, and events. This systematic review focuses on the evolving research area of Social Opinion Mining, tasked with the identification of multiple opinion dimensions, such as subjectivity, sentiment polarity, emotion, affect, sarcasm and irony, from user-generated content represented across multiple social media platforms and in various media formats, like text, image, video and audio. Therefore, through Social Opinion Mining, natural language can be understood in terms of the different opinion dimensions, as expressed by humans. This contributes towards the evolution of Artificial Intelligence, which in turn helps the advancement of several real-world use cases, such as customer service and decision making. A thorough systematic review was carried out on Social Opinion Mining research which totals 485 studies and spans a period of twelve years between 2007 and 2018. The in-depth analysis focuses on the social media platforms, techniques, social datasets, language, modality, tools and technologies, natural language processing tasks and other aspects derived from the published studies. Such multi-source information fusion plays a fundamental role in mining of people's social opinions from social media platforms. These can be utilised in many application areas, ranging from marketing, advertising and sales for product/service management, and in multiple domains and industries, such as politics, technology, finance, healthcare, sports and government. Future research directions are presented, whereas further research and development has the potential of leaving a wider academic and societal impact.