Meta-learning has proven to be successful at few-shot learning across the regression, classification and reinforcement learning paradigms. Recent approaches have adopted Bayesian interpretations to improve gradient based meta-learners by quantifying the uncertainty of the post-adaptation estimates. Most of these works almost completely ignore the latent relationship between the covariate distribution (p(x)) of a task and the corresponding conditional distribution p(y|x). In this paper, we identify the need to explicitly model the meta-distribution over the task covariates in a hierarchical Bayesian framework. We begin by introducing a graphical model that explicitly leverages very few samples drawn from p(x) to better infer the posterior over the optimal parameters of the conditional distribution (p(y|x)) for each task. Based on this model we provide an inference strategy and a corresponding meta-algorithm that explicitly accounts for the meta-distribution over task covariates. Finally, we demonstrate the significant gains of our proposed algorithm on a synthetic regression dataset.

Dynamic Bayesian networks have been well explored in the literature as discrete-time models; however, their continuous-time extensions have seen comparatively little attention. In this paper, we propose the first constraint-based algorithm for learning the structure of continuous-time Bayesian networks. We discuss the different statistical tests and the underlying hypotheses used by our proposal to establish conditional independence. Finally, we validate its performance using synthetic data, and discuss its strengths and limitations. We find that score-based is more accurate in learning networks with binary variables, while our constraint-based approach is more accurate with variables assuming more than two values. However, more experiments are needed for confirmation.

Precision farming is one way of many to meet a 70 percent increase in global demand for agricultural products on current agricultural land by 2050 at reduced need of fertilizers and efficient use of water resources. The catalyst for the emergence of precision farming has been satellite positioning and navigation followed by Internet-of-Things, generating vast information that can be used to optimize farming processes in real-time. Statistical tools from data mining, predictive modeling, and machine learning analyze pattern in historical data, to make predictions about future events as well as intelligent actions. This special issue presents the latest development in statistical inference, machine learning and optimum control for precision farming.

This dissertation investigates integer linear programming (ILP) formulation of Bayesian Network structure learning problem. We review the definition and key properties of Bayesian network and explain score metrics used to measure how well certain Bayesian network structure fits the dataset. We outline the integer linear programming formulation based on the decomposability of score metrics. In order to ensure acyclicity of the structure, we add ``cluster constraints'' developed specifically for Bayesian network, in addition to cycle constraints applicable to directed acyclic graphs in general. Since there would be exponential number of these constraints if we specify them fully, we explain the methods to add them as cutting planes without declaring them all in the initial model. Also, we develop a heuristic algorithm that finds a feasible solution based on the idea of sink node on directed acyclic graphs. We implemented the ILP formulation and cutting planes as a \textsf{Python} package, and present the results of experiments with different settings on reference datasets.

This study presents a semi-nonparametric Latent Class Choice Model (LCCM) with a flexible class membership component. The proposed model formulates the latent classes using mixture models as an alternative approach to the traditional random utility specification with the aim of comparing the two approaches on various measures including prediction accuracy and representation of heterogeneity in the choice process. Mixture models are parametric model-based clustering techniques that have been widely used in areas such as machine learning, data mining and patter recognition for clustering and classification problems. An Expectation-Maximization (EM) algorithm is derived for the estimation of the proposed model. Using two different case studies on travel mode choice behavior, the proposed model is compared to traditional discrete choice models on the basis of parameter estimates' signs, value of time, statistical goodness-of-fit measures, and cross-validation tests. Results show that mixture models improve the overall performance of latent class choice models by providing better out-of-sample prediction accuracy in addition to better representations of heterogeneity without weakening the behavioral and economic interpretability of the choice models.

We study the problem of learning the Markov order in categorical sequences that represent paths in a network, i.e. sequences of variable lengths where transitions between states are constrained to a known graph. Such data pose challenges for standard Markov order detection methods and demand modelling techniques that explicitly account for the graph constraint. Adopting a multi-order modelling framework for paths, we develop a Bayesian learning technique that (i) more reliably detects the correct Markov order compared to a competing method based on the likelihood ratio test, (ii) requires considerably less data compared to methods using AIC or BIC, and (iii) is robust against partial knowledge of the underlying constraints. We further show that a recently published method that uses a likelihood ratio test has a tendency to overfit the true Markov order of paths, which is not the case for our Bayesian technique. Our method is important for data scientists analyzing patterns in categorical sequence data that are subject to (partially) known constraints, e.g. sequences with forbidden words, mobility trajectories and click stream data, or sequence data in bioinformatics. Addressing the key challenge of model selection, our work is further relevant for the growing body of research that emphasizes the need for higher-order models in network analysis.

As described in [1][2], time series data includes many kinds of real experimental data taken from various domains such as finance, medicine, scientific research (e.g., global warming, speech analysis, earthquakes), etc. Time series forecasting has many real applications in various areas such as forecasting of business (e.g., sales, stock), weather, decease, and others [2]. Statistical modeling and inference (e.g., ARIMA model) [1][2] is one of the popular methods for time series analysis and forecasting. The philosophy of Bayesian inference is to consider probability as a measure of believability in an event [3][4][5] and use Bayes' theorem to update the probability as more evidence or information becomes available, while the philosophy of frequentist inference considers probability as the long-run frequency of events [3]. Generally speaking, we can use the Frequentist inference only when a large number of data samples are available.

The Expected Free Energy (EFE) is a central quantity in the theory of active inference. It is the quantity that all active inference agents are mandated to minimize through action, and its decomposition into extrinsic and intrinsic value terms is key to the balance of exploration and exploitation that active inference agents evince. Despite its importance, the mathematical origins of this quantity and its relation to the Variational Free Energy (VFE) remain unclear. In this paper, we investigate the origins of the EFE in detail and show that it is not simply "the free energy in the future". We present a functional that we argue is the natural extension of the VFE, but which actively discourages exploratory behaviour, thus demonstrating that exploration does not directly follow from free energy minimization into the future. We then develop a novel objective, the Free-Energy of the Expected Future (FEEF), which possesses both the epistemic component of the EFE as well as an intuitive mathematical grounding as the divergence between predicted and desired futures.

These are the lecture notes for FAU's YouTube Lecture "Deep Learning". This is a full transcript of the lecture video & matching slides. We hope, you enjoy this as much as the videos. Of course, this transcript was created with deep learning techniques largely automatically and only minor manual modifications were performed. If you spot mistakes, please let us know!

Teleoperation of physically assistive machines is usually facilitated by interfaces that are low-dimensional and have unique physical mechanisms for their activation. Accidental deviations from intended user input commands due to motor limitations can potentially affect user satisfaction and task performance. In this paper, we present an assistance system that reasons about a human's intended actions during robot teleoperation in order to provide appropriate corrections for unintended behavior. We model the human's physical interaction with a control interface during robot teleoperation using the framework of dynamic Bayesian Networks in which we distinguish between intended and measured physical actions explicitly. By reasoning over the unobserved intentions using model-based inference techniques, our assistive system provides customized corrections on a user's issued commands. We present results from (1) a simulation-based study in which we validate our algorithm and (2) a 10-person human subject study in which we evaluate the performance of the proposed assistance paradigms. Our results suggest that (a) the corrective assistance paradigm helped to significantly reduce objective task effort as measured by task completion time and number of mode switches and (b) the assistance paradigms helped to reduce cognitive workload and user frustration and improve overall satisfaction.