It is well known that a small number of variables is often sufficient to effectively describe high-dimensional data. This number is called the intrinsic dimension (ID) of the data. What is not so commonly known is that the ID can vary within the same dataset. This fact has been highlighted in technical discussions, but seldom exploited to gain practical insight in the data structure. Here we develop a simple and robust approach to cluster regions with the same local ID in a given data landscape. Surprisingly, we find that many real-world data sets contain regions with widely heterogeneous dimensions. These regions host points differing in core properties: folded vs unfolded configurations in a protein molecular dynamics trajectory, active vs non-active regions in brain imaging data, and firms with different financial risk in company balance sheets. Our results show that a simple topological feature, the local ID, is sufficient to uncover a rich structure in high-dimensional data landscapes. Introduction From string theory to science fiction, the idea that we might be glued onto a lowdimensional surface embedded in a space of large dimensionality has tickled the speculations of scientists and writers alike. When it comes to multidimensional data, however, such situation is quite common rather than a wild speculation: data often concentrate on hypersurfaces of low intrinsic dimension (ID).

We provide a summary over architectural approaches that can be used to construct dependable learning-enabled autonomous systems, with a focus on automated driving. We consider three technology pillars for architecting dependable autonomy, namely diverse redundancy, information fusion, and runtime monitoring. For learning-enabled components, we additionally summarize recent architectural approaches to increase the dependability beyond standard convolutional neural networks. We conclude the study with a list of promising research directions addressing the challenges of existing approaches.

Increasing amounts of available data have led to a heightened need for representing large-scale probabilistic knowledge bases. One approach is to use a probabilistic database, a model with strong assumptions that allow for efficiently answering many interesting queries. Recent work on open-world probabilistic databases strengthens the semantics of these probabilistic databases by discarding the assumption that any information not present in the data must be false. While intuitive, these semantics are not sufficiently precise to give reasonable answers to queries. We propose overcoming these issues by using constraints to restrict this open world. We provide an algorithm for one class of queries, and establish a basic hardness result for another. Finally, we propose an efficient and tight approximation for a large class of queries.

This paper proposes a new classification model called logistic circuits. On MNIST and Fashion datasets, our learning algorithm outperforms neural networks that have an order of magnitude more parameters. Yet, logistic circuits have a distinct origin in symbolic AI, forming a discriminative counterpart to probabilistic-logical circuits such as ACs, SPNs, and PSDDs. We show that parameter learning for logistic circuits is convex optimization, and that a simple local search algorithm can induce strong model structures from data.

While Bayesian neural networks (BNNs) have drawn increasing attention, their posterior inference remains challenging, due to the high-dimensional and over-parameterized nature. To address this issue, several highly flexible and scalable variational inference procedures based on the idea of particle optimization have been proposed. These methods directly optimize a set of particles to approximate the target posterior. However, their application to BNNs often yields sub-optimal performance, as such methods have a particular failure mode on over-parameterized models. In this paper, we propose to solve this issue by performing particle optimization directly in the space of regression functions. We demonstrate through extensive experiments that our method successfully overcomes this issue, and outperforms strong baselines in a variety of tasks including prediction, defense against adversarial examples, and reinforcement learning.

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.