Clustering techniques have been proved highly suc-cessful for Takagi-Sugeno (T-S) fuzzy model identification. Inparticular, fuzzyc-regression clustering based on type-2 fuzzyset has been shown the remarkable results on non-sparse databut their performance degraded on sparse data. In this paper, aninnovative architecture for fuzzyc-regression model is presentedand a novel student-tdistribution based membership functionis designed for sparse data modelling. To avoid the overfitting,we have adopted a Bayesian approach for incorporating aGaussian prior on the regression coefficients. Additional noveltyof our approach lies in type-reduction where the final output iscomputed using Karnik Mendel algorithm and the consequentparameters of the model are optimized using Stochastic GradientDescent method. As detailed experimentation, the result showsthat proposed approach outperforms on standard datasets incomparison of various state-of-the-art methods.

In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the co-Kleisli category under the comonad (Omega x -) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identity-on-objects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood

We introduce a non-parametric hierarchical Bayesian approach for open-ended 3D object categorization, named the Local Hierarchical Dirichlet Process (Local-HDP). This method allows an agent to learn independent topics for each category incrementally and to adapt to the environment in time. Hierarchical Bayesian approaches like Latent Dirichlet Allocation (LDA) can transform low-level features to high-level conceptual topics for 3D object categorization. However, the efficiency and accuracy of LDA-based approaches depend on the number of topics that is chosen manually. Moreover, fixing the number of topics for all categories can lead to overfitting or underfitting of the model. In contrast, the proposed Local-HDP can autonomously determine the number of topics for each category. Furthermore, an inference method is proposed that results in a fast posterior approximation. Experiments show that Local-HDP outperforms other state-of-the-art approaches in terms of accuracy, scalability, and memory efficiency with a large margin.

Out-of-training-distribution (OOD) scenarios are a common challenge of learning agents at deployment, typically leading to arbitrary deductions and poorly-informed decisions. In principle, detection of and adaptation to OOD scenes can mitigate their adverse effects. In this paper, we highlight the limitations of current approaches to novel driving scenes and propose an epistemic uncertainty-aware planning method, called \emph{robust imitative planning} (RIP). Our method can detect and recover from some distribution shifts, reducing the overconfident and catastrophic extrapolations in OOD scenes. If the model's uncertainty is too great to suggest a safe course of action, the model can instead query the expert driver for feedback, enabling sample-efficient online adaptation, a variant of our method we term \emph{adaptive robust imitative planning} (AdaRIP). Our methods outperform current state-of-the-art approaches in the nuScenes \emph{prediction} challenge, but since no benchmark evaluating OOD detection and adaption currently exists to assess \emph{control}, we introduce an autonomous car novel-scene benchmark, \texttt{CARNOVEL}, to evaluate the robustness of driving agents to a suite of tasks with distribution shifts.

According to the similarity of the function and form of the algorithm, we can classify the algorithm, such as tree-based algorithm, neural network-based algorithm, and so on. Of course, the scope of machine learning is very large, and it is difficult for some algorithms to be clearly classified into a certain category. Regression algorithm is a type of algorithm that tries to explore the relationship between variables by using a measure of error. Regression algorithm is a powerful tool for statistical machine learning. In the field of machine learning, when people talk about regression, sometimes they refer to a type of problem and sometimes a type of algorithm.

Emergency response to incidents such as accidents, medical calls, and fires is one of the most pressing problems faced by communities across the globe. In the last fifty years, researchers have developed statistical, analytical, and algorithmic approaches for designing emergency response management (ERM) systems. In this survey, we present models for incident prediction, resource allocation, and dispatch for emergency incidents. We highlight the strengths and weaknesses of prior work in this domain and explore the similarities and differences between different modeling paradigms. Finally, we present future research directions. To the best of our knowledge, our work is the first comprehensive survey that explores the entirety of ERM systems.

Modern machine learning applications should be able to address the intrinsic challenges arising over inference on massive real-world datasets, including scalability and robustness to outliers. Despite the multiple benefits of Bayesian methods (such as uncertainty-aware predictions, incorporation of experts knowledge, and hierarchical modeling), the quality of classic Bayesian inference depends critically on whether observations conform with the assumed data generating model, which is impossible to guarantee in practice. In this work, we propose a variational inference method that, in a principled way, can simultaneously scale to large datasets, and robustify the inferred posterior with respect to the existence of outliers in the observed data. Reformulating Bayes theorem via the $\beta$-divergence, we posit a robustified pseudo-Bayesian posterior as the target of inference. Moreover, relying on the recent formulations of Riemannian coresets for scalable Bayesian inference, we propose a sparse variational approximation of the robustified posterior and an efficient stochastic black-box algorithm to construct it. Overall our method allows releasing cleansed data summaries that can be applied broadly in scenarios including structured data corruption. We illustrate the applicability of our approach in diverse simulated and real datasets, and various statistical models, including Gaussian mean inference, logistic and neural linear regression, demonstrating its superiority to existing Bayesian summarization methods in the presence of outliers.

Protein contacts provide key information for the understanding of protein structure and function, and therefore contact prediction from sequences is an important problem. Recent research shows that some correctly predicted long-range contacts could help topology-level structure modeling. Thus, contact prediction and contact-assisted protein folding also proves the importance of this problem. In this thesis, I will briefly introduce the extant related work, then show how to establish the contact prediction through unsupervised graphical models with topology constraints. Further, I will explain how to use the supervised deep learning methods to further boost the accuracy of contact prediction. Finally, I will propose a scoring system called diversity score to measure the novelty of contact predictions, as well as an algorithm that predicts contacts with respect to the new scoring system.

As the name says, these approaches rely on the availability of data to extract knowledge and train algorithms. This is opposed to, e.g., modeling approaches in which physiological, physics-based, mathematical, and other equations form the basis of algorithms, or, rule-based systems in which reasoning processes are obtained by translating domain-experts' knowledge into computer-based rules. Focusing on data-driven systems, the data plays a role in several components during the development and actual usage phases. First, we need data to extract knowledge from, i.e., to develop and train algorithms so that they learn-by-example the properties of the problem at hand and get better at solving the problem by repeatedly providing example data. Second, we need to monitor during the development phase how promising the algorithms are and make choices, e.g., concerning optimisation of parameters or choosing different MLparadigms. Methods that don't perform well at all can be discarded, and ones that seem promising can be further optimised. To assess how promising a specific method is, we need to examine how it performs on data that was not used during training. Finally, to objectively assess how well the final'best' system performs, we need to apply completely new data to it that has not been used at all thusfar during the research and development process. Thus, there are at least three stakeholders that have the interest to get as large part of the data pie as possible.

In nuclear engineering, modeling and simulations (M&Ss) are widely applied to support risk-informed safety analysis. Since nuclear safety analysis has important implications, a convincing validation process is needed to assess simulation adequacy, i.e., the degree to which M&S tools can adequately represent the system quantities of interest. However, due to data gaps, validation becomes a decision-making process under uncertainties. Expert knowledge and judgments are required to collect, choose, characterize, and integrate evidence toward the final adequacy decision. However, in validation frameworks CSAU: Code Scaling, Applicability, and Uncertainty (NUREG/CR-5249) and EMDAP: Evaluation Model Development and Assessment Process (RG 1.203), such a decision-making process is largely implicit and obscure. When scenarios are complex, knowledge biases and unreliable judgments can be overlooked, which could increase uncertainty in the simulation adequacy result and the corresponding risks. Therefore, a framework is required to formalize the decision-making process for simulation adequacy in a practical, transparent, and consistent manner. This paper suggests a framework "Predictive Capability Maturity Quantification using Bayesian network (PCMQBN)" as a quantified framework for assessing simulation adequacy based on information collected from validation activities. A case study is prepared for evaluating the adequacy of a Smoothed Particle Hydrodynamic simulation in predicting the hydrodynamic forces onto static structures during an external flooding scenario. Comparing to the qualitative and implicit adequacy assessment, PCMQBN is able to improve confidence in the simulation adequacy result and to reduce expected loss in the risk-informed safety analysis.