In this article, we present a novel approach to multivariate probabilistic forecasting. Our approach is based on an extension of single-output quantile regression (QR) to multivariate-targets, called quantile surfaces (QS). QS uses a simple yet compelling idea of indexing observations of a probabilistic forecast through direction and vector length to estimate a central tendency. We extend the single-output QR technique to multivariate probabilistic targets. QS efficiently models dependencies in multivariate target variables and represents probability distributions through discrete quantile levels. Therefore, we present a novel two-stage process. In the first stage, we perform a deterministic point forecast (i.e., central tendency estimation). Subsequently, we model the prediction uncertainty using QS involving neural networks called quantile surface regression neural networks (QSNN). Additionally, we introduce new methods for efficient and straightforward evaluation of the reliability and sharpness of the issued probabilistic QS predictions. We complement this by the directional extension of the Continuous Ranked Probability Score (CRPS) score. Finally, we evaluate our novel approach on synthetic data and two currently researched real-world challenges in two different domains: First, probabilistic forecasting for renewable energy power generation, second, short-term cyclists trajectory forecasting for autonomously driving vehicles. Especially for the latter, our empirical results show that even a simple one-layer QSNN outperforms traditional parametric multivariate forecasting techniques, thus improving the state-of-the-art performance.

Recent progress in artificial intelligence provides the opportunity to ask the question of what is unique about human intelligence, but with a new comparison class. I argue that we can understand human intelligence, and the ways in which it may di er from artificial intelligence, by considering the characteristics of the kind of computational problems that human minds have to solve. I claim that these problems acquire their structure from three fundamental limitations that apply to human beings: limited time, limited computation, and limited communication. From these limitations we can derive many of the properties we associate with human intelligence, such as rapid learning, the ability to break down problems into parts, and the capacity for cumulative cultural evolution. Understanding Human Intelligence through Human Limitations Di erent Computational Problems, Di erent Kinds of Intelligence As machines begin to outperform humans on an increasing number of tasks, it is natural to ask what is unique about human intelligence. Historically, this has been a question that is asked when comparing humans to other animals. The classical answer (from Aristotle, via the Scholastics) is to view humans as "rational animals" - animals that think [18]. More modern analyses of human uniqueness emphasize the "cognitive niche" that humans fill, able to use their minds to outsmart the biological defenses of their competitors [43], or contrast this with the "cultural niche" of being able to accumulate knowledge across individuals and generations in a way that makes it possible to live in an unusually diverse range of environments [10, 25, 26]. Asking the same question of what makes humans unique, but changing the contrast class to include intelligent machines, yields a very di erent kind of answer. In this article I argue that even as we develop potentially superhuman machines, there is going to be a flavor of intelligence that remains uniquely human.

Deep learning approaches to anomaly detection have recently improved the state of the art in detection performance on complex datasets such as large collections of images or text. These results have sparked a renewed interest in the anomaly detection problem and led to the introduction of a great variety of new methods. With the emergence of numerous such methods, including approaches based on generative models, one-class classification, and reconstruction, there is a growing need to bring methods of this field into a systematic and unified perspective. In this review we aim to identify the common underlying principles as well as the assumptions that are often made implicitly by various methods. In particular, we draw connections between classic 'shallow' and novel deep approaches and show how this relation might cross-fertilize or extend both directions. We further provide an empirical assessment of major existing methods that is enriched by the use of recent explainability techniques, and present specific worked-through examples together with practical advice. Finally, we outline critical open challenges and identify specific paths for future research in anomaly detection.

Regularization improves generalization of supervised models to out-of-sample data. Prior works have shown that prediction in the causal direction (effect from cause) results in lower testing error than the anti-causal direction. However, existing regularization methods are agnostic of causality. We introduce Causal Structure Learning (CASTLE) regularization and propose to regularize a neural network by jointly learning the causal relationships between variables. CASTLE learns the causal directed acyclical graph (DAG) as an adjacency matrix embedded in the neural network's input layers, thereby facilitating the discovery of optimal predictors. Furthermore, CASTLE efficiently reconstructs only the features in the causal DAG that have a causal neighbor, whereas reconstruction-based regularizers suboptimally reconstruct all input features. We provide a theoretical generalization bound for our approach and conduct experiments on a plethora of synthetic and real publicly available datasets demonstrating that CASTLE consistently leads to better out-of-sample predictions as compared to other popular benchmark regularizers.

In this paper, we consider mixtures of multinomial logistic models (MNL), which are known to $\epsilon$-approximate any random utility model. Despite its long history and broad use, rigorous results are only available for learning a uniform mixture of two MNLs. Continuing this line of research, we study the problem of learning an arbitrary mixture of two MNLs. We show that the identifiability of the mixture models may only fail on an algebraic variety of a negligible measure. This is done by reducing the problem of learning a mixture of two MNLs to the problem of solving a system of univariate quartic equations. We also devise an algorithm to learn any mixture of two MNLs using a polynomial number of samples and a linear number of queries, provided that a mixture of two MNLs over some finite universe is identifiable. Several numerical experiments and conjectures are also presented.

Linear logic [Gir87] comprises a rich and fascinating formal system that summarizes, in a nuanced way, the way logical inference works if one treats the pool of potential premises of inferences as a resource to be meted out and accounted for. The linear logic abstractions can be applied to practical reasoning systems in a variety of different ways, and can be grounded in concrete domain-specific inference formalisms via multiple routes as well. Here we connect linear logic to uncertain reasoning based on observational semantics. Beginning with a simple semantics for propositions, based on counting observations, we argue that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence bases are not currently available. These two different heuristic assumptions lead to two different sets of formulas for propagating quantitative truth values through lattice operations. Given this setup, it becomes immediately apparents that these two sets of formulas instantiate the same algebraic and conceptual relationships as the multiplicative and additive operator-sets in linear logic. The standard rules of linear logic then emerge as consequences of the underlying semantics of fuzzy and probabilistic evidence management.

Performing efficient inference on high dimensional discrete Bayesian Networks (BNs) is challenging. When using exact inference methods the space complexity can grow exponentially with the tree-width, thus making computation intractable. This paper presents a general purpose approximate inference algorithm, based on a new region belief approximation method, called Triplet Region Construction (TRC). TRC reduces the cluster space complexity for factorized models from worst-case exponential to polynomial by performing graph factorization and producing clusters of limited size. Unlike previous generations of region-based algorithms, TRC is guaranteed to converge and effectively addresses the region choice problem that bedevils other region-based algorithms used for BN inference. Our experiments demonstrate that it also achieves significantly more accurate results than competing algorithms.

This paper studies the problem of learning the correlation structure of a set of intervention functions defined on the directed acyclic graph (DAG) of a causal model. This is useful when we are interested in jointly learning the causal effects of interventions on different subsets of variables in a DAG, which is common in field such as healthcare or operations research. We propose the first multi-task causal Gaussian process (GP) model, which we call DAG-GP, that allows for information sharing across continuous interventions and across experiments on different variables. DAG-GP accommodates different assumptions in terms of data availability and captures the correlation between functions lying in input spaces of different dimensionality via a well-defined integral operator. We give theoretical results detailing when and how the DAG-GP model can be formulated depending on the DAG. We test both the quality of its predictions and its calibrated uncertainties. Compared to single-task models, DAG-GP achieves the best fitting performance in a variety of real and synthetic settings. In addition, it helps to select optimal interventions faster than competing approaches when used within sequential decision making frameworks, like active learning or Bayesian optimization.

We address the question of characterizing and finding optimal representations for supervised learning. Traditionally, this question has been tackled using the Information Bottleneck, which compresses the inputs while retaining information about the targets, in a decoder-agnostic fashion. In machine learning, however, our goal is not compression but rather generalization, which is intimately linked to the predictive family or decoder of interest (e.g. linear classifier). We propose the Decodable Information Bottleneck (DIB) that considers information retention and compression from the perspective of the desired predictive family. As a result, DIB gives rise to representations that are optimal in terms of expected test performance and can be estimated with guarantees. Empirically, we show that the framework can be used to enforce a small generalization gap on downstream classifiers and to predict the generalization ability of neural networks.

Evidential clustering is an approach to clustering based on the use of Dempster-Shafer mass functions to represent cluster-membership uncertainty. In this paper, we introduce a neural-network based evidential clustering algorithm, called NN-EVCLUS, which learns a mapping from attribute vectors to mass functions, in such a way that more similar inputs are mapped to output mass functions with a lower degree of conflict. The neural network can be paired with a one-class support vector machine to make it robust to outliers and allow for novelty detection. The network is trained to minimize the discrepancy between dissimilarities and degrees of conflict for all or some object pairs. Additional terms can be added to the loss function to account for pairwise constraints or labeled data, which can also be used to adapt the metric. Comparative experiments show the superiority of N-EVCLUS over state-of-the-art evidential clustering algorithms for a range of unsupervised and constrained clustering tasks involving both attribute and dissimilarity data.