The subject of this article is the introduction of a weaker concept of well-posedness of Bayesian inverse problems. The conventional concept of (`Lipschitz') well-posedness in [Stuart 2010, Acta Numerica 19, pp. 451-559] is difficult to verify in practice, especially when considering blackbox models, and probably too strong in many contexts. Our concept replaces the Lipschitz continuity of the posterior measure in the Hellinger distance by just continuity. This weakening is tolerable, since the continuity is in general only used as a stability criterion. The main result of this article is a proof of well-posedness for a large class of Bayesian inverse problems, where very little or no information about the underlying model is available. It includes any Bayesian inverse problem arising when observing finite-dimensional data perturbed by additive, non-degenerate Gaussian noise. Moreover, well-posedness with respect to other probability metrics is investigated, including weak convergence, total variation, Wasserstein, and also the Kullback-Leibler divergence.

Modern systems (e.g., deep neural networks, big data analytics, and compilers) are highly configurable, which means they expose different performance behavior under different configurations. The fundamental challenge is that one cannot simply measure all configurations due to the sheer size of the configuration space. Transfer learning has been used to reduce the measurement efforts by transferring knowledge about performance behavior of systems across environments. Previously, research has shown that statistical models are indeed transferable across environments. In this work, we investigate identifiability and transportability of causal effects and statistical relations in highly-configurable systems. Our causal analysis agrees with previous exploratory analysis \cite{Jamshidi17} and confirms that the causal effects of configuration options can be carried over across environments with high confidence. We expect that the ability to carry over causal relations will enable effective performance analysis of highly-configurable systems.

These two limitations have been thoroughly Banded matrices can be used as precision studied over the past decades and several approaches matrices in several models including linear have been proposed to overcome them. The most popular state-space models, some Gaussian processes, method for reducing computational complexity is and Gaussian Markov random fields. The the sparse GP framework (Candela and Rasmussen, aim of the paper is to make modern inference 2005; Titsias, 2009), where computations are focussed methods (such as variational inference or on a set of "inducing variables", allowing a tradeoff gradient-based sampling) available for Gaussian between computational requirements and the accuracy models with banded precision.

Missing values frequently arise in modern biomedical studies due to various reasons, including missing tests or complex profiling technologies for different omics measurements. Missing values can complicate the application of clustering algorithms, whose goals are to group points based on some similarity criterion. A common practice for dealing with missing values in the context of clustering is to first impute the missing values, and then apply the clustering algorithm on the completed data. We consider missing values in the context of optimal clustering, which finds an optimal clustering operator with reference to an underlying random labeled point process (RLPP). We show how the missing-value problem fits neatly into the overall framework of optimal clustering by incorporating the missing value mechanism into the random labeled point process and then marginalizing out the missing-value process. In particular, we demonstrate the proposed framework for the Gaussian model with arbitrary covariance structures. Comprehensive experimental studies on both synthetic and real-world RNA-seq data show the superior performance of the proposed optimal clustering with missing values when compared to various clustering approaches. Optimal clustering with missing values obviates the need for imputation-based pre-processing of the data, while at the same time possessing smaller clustering errors.

Finding an optimal parameter of a black-box function is important for searching stable material structures and finding optimal neural network structures, and Bayesian optimization algorithms are widely used for the purpose. However, most of existing Bayesian optimization algorithms can only handle vector data and cannot handle complex structured data. In this paper, we propose the topological Bayesian optimization, which can efficiently find an optimal solution from structured data using \emph{topological information}. More specifically, in order to apply Bayesian optimization to structured data, we extract useful topological information from a structure and measure the proper similarity between structures. To this end, we utilize persistent homology, which is a topological data analysis method that was recently applied in machine learning. Moreover, we propose the Bayesian optimization algorithm that can handle multiple types of topological information by using a linear combination of kernels for persistence diagrams. Through experiments, we show that topological information extracted by persistent homology contributes to a more efficient search for optimal structures compared to the random search baseline and the graph Bayesian optimization algorithm.

Interpretability has always been a major concern for fuzzy rule-based classifiers. The usage of human-readable models allows them to explain the reasoning behind their predictions and decisions. However, when it comes to Big Data classification problems, fuzzy rule-based classifiers have not been able to maintain the good trade-off between accuracy and interpretability that has characterized these techniques in non-Big Data environments. The most accurate methods build too complex models composed of a large number of rules and fuzzy sets, while those approaches focusing on interpretability do not provide state-of-the-art discrimination capabilities. In this paper, we propose a new distributed learning algorithm named CFM-BD to construct accurate and compact fuzzy rule-based classification systems for Big Data. This method has been specifically designed from scratch for Big Data problems and does not adapt or extend any existing algorithm. The proposed learning process consists of three stages: 1) pre-processing based on the probability integral transform theorem; 2) rule induction inspired by CHI-BD and Apriori algorithms; 3) rule selection by means of a global evolutionary optimization. We conducted a complete empirical study to test the performance of our approach in terms of accuracy, complexity, and runtime. The results obtained were compared and contrasted with four state-of-the-art fuzzy classifiers for Big Data (FBDT, FMDT, Chi-Spark-RS, and CHI-BD). According to this study, CFM-BD is able to provide competitive discrimination capabilities using significantly simpler models composed of a few rules of less than 3 antecedents, employing 5 linguistic labels for all variables.

We propose a developmental approach that allows a robot to interpret and describe the actions of human agents by reusing previous experience. The robot first learns the association between words and object affordances by manipulating the objects in its environment. It then uses this information to learn a mapping between its own actions and those performed by a human in a shared environment. It finally fuses the information from these two models to interpret and describe human actions in light of its own experience. In our experiments, we show that the model can be used flexibly to do inference on different aspects of the scene. We can predict the effects of an action on the basis of object properties. We can revise the belief that a certain action occurred, given the observed effects of the human action. In an early action recognition fashion, we can anticipate the effects when the action has only been partially observed. By estimating the probability of words given the evidence and feeding them into a pre-defined grammar, we can generate relevant descriptions of the scene. We believe that this is a step towards providing robots with the fundamental skills to engage in social collaboration with humans.

Recent advances in conditional image generation tasks, such as image-to-image translation and image inpainting, are largely accounted to the success of conditional GAN models, which are often optimized by the joint use of the GAN loss with the reconstruction loss However, we reveal that this training recipe shared by almost all existing methods causes one critical side effect: lack of diversity in output samples. In order to accomplish both training stability and multimodal output generation, we propose novel training schemes with a new set of losses named moment reconstruction losses that simply replace the reconstruction loss. We show that our approach is applicable to any conditional generation tasks by performing thorough experiments on image-to-image translation, super-resolution and image inpainting using Cityscapes and CelebA dataset. Quantitative evaluations also confirm that our methods achieve a great diversity in outputs while retaining or even improving the visual fidelity of generated samples. Recently, active research has led to a huge progress on conditional image generation, whose typical tasks include image-to-image translation (Isola et al. (2017)), image inpainting (Pathak et al. (2016)), super-resolution (Ledig et al. (2017)) and video prediction (Mathieu et al. (2016)). At the core of such advances is the success of conditional GANs (Mirza & Osindero (2014)), which improve GANs by allowing the generator to take an additional code or condition to control the modes of the data being generated. However, training GANs, including conditional GANs, is highly unstable and easy to collapse (Goodfellow et al. (2014)). Indeed, using these two types of losses is synergetic in that the GAN loss complements the weakness of the reconstruction loss that output samples are blurry and lack high-frequency structure, while the reconstruction loss offers the training stability required for convergence. In spite of its success, we argue that it causes one critical side effect; the reconstruction loss aggravates the mode collapse, one of notorious problems of GANs. In conditional generation tasks, which are to intrinsically learn one-to-many mappings, the model is expected to generate diverse outputs from a single conditional input, depending on some stochastic variables (e.g.

With the increasing variety of services that e-commerce platforms provide, criteria for evaluating their success become also increasingly multi-targeting. This work introduces a multi-target optimization framework with Bayesian modeling of the target events, called Deep Bayesian Multi-Target Learning (DBMTL). In this framework, target events are modeled as forming a Bayesian network, in which directed links are parameterized by hidden layers, and learned from training samples. The structure of Bayesian network is determined by model selection. We applied the framework to Taobao live-streaming recommendation, to simultaneously optimize (and strike a balance) on targets including click-through rate, user stay time in live room, purchasing behaviors and interactions. Significant improvement has been observed for the proposed method over other MTL frameworks and the non-MTL model. Our practice shows that with an integrated causality structure, we can effectively make the learning of a target benefit from other targets, creating significant synergy effects that improve all targets. The neural network construction guided by DBMTL fits in with the general probabilistic model connecting features and multiple targets, taking weaker assumption than the other methods discussed in this paper. This theoretical generality brings about practical generalization power over various targets distributions, including sparse targets and continuous-value ones.

Traditional models of rational action treat the agent as though it is cleanly separated from its environment, and can act on that environment from the outside. Such agents have a known functional relationship with their environment, can model their environment in every detail, and do not need to reason about themselves or their internal parts. We provide an informal survey of obstacles to formalizing good reasoning for agents embedded in their environment. Such agents must optimize an environment that is not of type ``function''; they must rely on models that fit within the modeled environment; and they must reason about themselves as just another physical system, made of parts that can be modified and that can work at cross purposes.