We introduce graph gamma process (GGP) linear dynamical systems to model real-valued multivariate time series. For temporal pattern discovery, the latent representation under the model is used to decompose the time series into a parsimonious set of multivariate sub-sequences. In each sub-sequence, different data dimensions often share similar temporal patterns but may exhibit distinct magnitudes, and hence allowing the superposition of all sub-sequences to exhibit diverse behaviors at different data dimensions. We further generalize the proposed model by replacing the Gaussian observation layer with the negative binomial distribution to model multivariate count time series. Generated from the proposed GGP is an infinite dimensional directed sparse random graph, which is constructed by taking the logical OR operation of countably infinite binary adjacency matrices that share the same set of countably infinite nodes. Each of these adjacency matrices is associated with a weight to indicate its activation strength, and places a finite number of edges between a finite subset of nodes belonging to the same node community. We use the generated random graph, whose number of nonzero-degree nodes is finite, to define both the sparsity pattern and dimension of the latent state transition matrix of a (generalized) linear dynamical system. The activation strength of each node community relative to the overall activation strength is used to extract a multivariate sub-sequence, revealing the data pattern captured by the corresponding community. On both synthetic and real-world time series, the proposed nonparametric Bayesian dynamic models, which are initialized at random, consistently exhibit good predictive performance in comparison to a variety of baseline models, revealing interpretable latent state transition patterns and decomposing the time series into distinctly behaved sub-sequences.

Graph-based semi-supervised regression (SSR) is the problem of estimating the value of a function on a weighted graph from its values (labels) on a small subset of the vertices. This paper is concerned with the consistency of SSR in the context of classification, in the setting where the labels have small noise and the underlying graph weighting is consistent with well-clustered nodes. We present a Bayesian formulation of SSR in which the weighted graph defines a Gaussian prior, using a graph Laplacian, and the labeled data defines a likelihood. We analyze the rate of contraction of the posterior measure around the ground truth in terms of parameters that quantify the small label error and inherent clustering in the graph. We obtain bounds on the rates of contraction and illustrate their sharpness through numerical experiments. The analysis also gives insight into the choice of hyperparameters that enter the definition of the prior.

Sequential decision making, commonly formalized as Markov Decision Process (MDP) optimization, is a key challenge in artificial intelligence. Two key approaches to this problem are reinforcement learning (RL) and planning. This paper presents a survey of the integration of both fields, better known as model-based reinforcement learning. Model-based RL has two main steps. First, we systematically cover approaches to dynamics model learning, including challenges like dealing with stochasticity, uncertainty, partial observability, and temporal abstraction. Second, we present a systematic categorization of planning-learning integration, including aspects like: where to start planning, what budgets to allocate to planning and real data collection, how to plan, and how to integrate planning in the learning and acting loop. After these two key sections, we also discuss the potential benefits of model-based RL, like enhanced data efficiency, targeted exploration, and improved stability. Along the survey, we also draw connections to several related RL fields, like hierarchical RL and transfer, and other research disciplines, like behavioural psychology. Altogether, the survey presents a broad conceptual overview of planning-learning combinations for MDP optimization.

In the causal learning setting, we wish to learn cause-and-effect relationships between variables such that we can correctly infer the effect of an intervention. While the difference between a cyclic structure and an acyclic structure may be just a single edge, cyclic causal structures have qualitatively different behavior under intervention: cycles cause feedback loops when the downstream effect of an intervention propagates back to the source variable. We present three theoretical observations about probability distributions with self-referential factorizations, i.e. distributions that could be graphically represented with a cycle. First, we prove that self-referential distributions in two variables are, in fact, independent. Second, we prove that self-referential distributions in N variables have zero mutual information. Lastly, we prove that self-referential distributions that factorize in a cycle, also factorize as though the cycle were reversed. These results suggest that cyclic causal dependence may exist even where observational data suggest independence among variables. Methods based on estimating mutual information, or heuristics based on independent causal mechanisms, are likely to fail to learn cyclic casual structures. We encourage future work in causal learning that carefully considers cycles.

The simplest solutions are usually the most powerful ones, and Naïve Bayes is a good example of that. Despite the advances in Machine Learning in the last years, it has proven to not only be simple but also fast, accurate, and reliable. It has been successfully used for many purposes, but it works particularly well with natural language processing (NLP) problems. Naïve Bayes is a probabilistic machine learning algorithm based on the Bayes Theorem, used in a wide variety of classification tasks. In this article, we will understand the Naïve Bayes algorithm and all essential concepts so that there is no room for doubts in understanding.

Gaussian ODE filtering is a probabilistic numerical method to solve ordinary differential equations (ODEs). It computes a Bayesian posterior over the solution from evaluations of the vector field defining the ODE. Its most popular version, which employs an integrated Brownian motion prior, uses Taylor expansions of the mean to extrapolate forward and has the same convergence rates as classical numerical methods. As the solution of many important ODEs are periodic functions (oscillators), we raise the question whether Fourier expansions can also be brought to bear within the framework of Gaussian ODE filtering. To this end, we construct a Fourier state space model for ODEs and a `hybrid' model that combines a Taylor (Brownian motion) and Fourier state space model. We show by experiments how the hybrid model might become useful in cheaply predicting until the end of the time domain.

The scope of a lucrative career promoted by Google through its video distribution platform YouTube has attracted a large number of users to become content creators. An important aspect of this line of work is the feedback received in the form of comments which show how well the content is being received by the audience. However, volume of comments coupled with spam and limited tools for comment classification makes it virtually impossible for a creator to go through each and every comment and gather constructive feedback. Automatic classification of comments is a challenge even for established classification models, since comments are often of variable lengths riddled with slang, symbols and abbreviations. This is a greater challenge where comments are multilingual as the messages are often rife with the respective vernacular. In this work, we have evaluated top-performing classification models for classifying comments which are a mix of different combinations of English and Malayalam (only English, only Malayalam and Mix of English and Malayalam). The statistical analysis of results indicates that Multinomial Naive Bayes, K-Nearest Neighbors (KNN), Support Vector Machine (SVM), Random Forest and Decision Trees offer similar level of accuracy in comment classification. Further, we have also evaluated 3 multilingual transformer based language models (BERT, DISTILBERT and XLM) and compared their performance to the traditional machine learning classification techniques. XLM was the top-performing BERT model with an accuracy of 67.31. Random Forest with Term Frequency Vectorizer was the best performing model out of all the traditional classification models with an accuracy of 63.59.

The ability to learn effective transformations of complex data sources, sometimes called representation learning, is an essential primitive in modern machine learning, leading to remarkable achievements in language modeling, vision, and serving as a partial explanation for the success of deep learning more broadly (Bengio et al., 2013). In Reinforcement Learning (RL), several works have shown empirically that learning succinct representations of perceptual inputs can accelerate the search for decision-making policies (Pathak et al., 2017; Tang et al., 2017; Oord et al., 2018; Srinivas et al., 2020). However, representation learning for RL is far more subtle than it is for supervised learning (Du et al., 2019a; Van Roy and Dong, 2019; Lattimore and Szepesvari, 2019), and the theoretical foundations of representation learning for RL are nascent. The first question that arises in this context is: what is a good representation? Intuitively, a good representation should help us achieve greater sample efficiency on downstream tasks.

There are multiple ways to estimate a Stan model in R, but I choose to build the Stan code directly rather than using the brms or rstanarm packages. In the Stan code, we need to define the data structure, specify the parameters, specify any transformed parameters (which are just a function of the parameters), and then build the model – which includes laying out the prior distributions as well as the likelihood. In this case, the model is slightly different from what was presented in the context of a mixed effects model. The key difference is that there are prior distributions on \(\Delta\) and \(\tau\), introducing an additional level of uncertainty into the estimate. I would expect that the estimate of the overall treatment effect \(\Delta\) will have a wider 95% CI (credible interval in this context) than the 95% CI (confidence interval) for \(\delta_0\) in the mixed effects model.

The use of sophisticated machine learning models for critical decision making is faced with a challenge that these models are often applied as a "black-box". This has led to an increased interest in interpretable machine learning, where post hoc interpretation presents a useful mechanism for generating interpretations of complex learning models. In this paper, we propose a novel approach underpinned by an extended framework of Bayesian networks for generating post hoc interpretations of a black-box predictive model. The framework supports extracting a Bayesian network as an approximation of the black-box model for a specific prediction. Compared to the existing post hoc interpretation methods, the contribution of our approach is three-fold. Firstly, the extracted Bayesian network, as a probabilistic graphical model, can provide interpretations about not only what input features but also why these features contributed to a prediction. Secondly, for complex decision problems with many features, a Markov blanket can be generated from the extracted Bayesian network to provide interpretations with a focused view on those input features that directly contributed to a prediction. Thirdly, the extracted Bayesian network enables the identification of four different rules which can inform the decision-maker about the confidence level in a prediction, thus helping the decision-maker assess the reliability of predictions learned by a black-box model. We implemented the proposed approach, applied it in the context of two well-known public datasets and analysed the results, which are made available in an open-source repository.