Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically need to be estimated from the dataset. This article provides one of the first theoretical analyses in the context of Gaussian process regression with a noiseless dataset. Specifically, we consider the scenario where the scale parameter of a Sobolev kernel (such as a Mat\'ern kernel) is estimated by maximum likelihood. We show that the maximum likelihood estimation of the scale parameter alone provides significant adaptation against misspecification of the Gaussian process model in the sense that the model can become "slowly" overconfident at worst, regardless of the difference between the smoothness of the data-generating function and that expected by the model. The analysis is based on a combination of techniques from nonparametric regression and scattered data interpolation. Empirical results are provided in support of the theoretical findings.

Incorporating constraints is a major concern in probabilistic machine learning. A wide variety of problems require predictions to be integrated with reasoning about constraints, from modelling routes on maps to approving loan predictions. In the former, we may require the prediction model to respect the presence of physical paths between the nodes on the map, and in the latter, we may require that the prediction model respect fairness constraints that ensure that outcomes are not subject to bias. Broadly speaking, constraints may be probabilistic, logical or causal, but the overarching challenge is to determine if and how a model can be learnt that handles all the declared constraints. To the best of our knowledge, this is largely an open problem. In this paper, we consider a mathematical inquiry on how the learning of tractable probabilistic models, such as sum-product networks, is possible while incorporating constraints.

stream-learn is a Python package compatible with scikit-learn and developed for the drifting and imbalanced data stream analysis. I ts main component is a stream generator, which allows to produce a synthet ic data stream that may incorporate each of the three main concept drift typ es (i.e. The package allows conducting experiments following estab lished evaluation methodologies (i.e. In addition, estimators adapted for data stream classification have been implem ented, including both simple classifiers and state-of-art chunk-based and online classifier ensembles. To improve computational efficiency, package utili ses its own implementations of prediction metrics for imbalanced binary cla ssification tasks. Keywords: Data stream, Concept drift, Imbalanced data, Dynamic class imbalance 1. Motivation and significance Pattern recognition research increasingly goes beyond the usual pattern of building classification models on stationary data sets an d focuses on data stream processing where class distributions, and hence als o decision boundaries, may change over time [1].

The key distinguishing property of a Bayesian approach is marginalization instead of optimization, not the prior, or Bayes rule. Bayesian inference is especially compelling for deep neural networks. (1) Neural networks are typically underspecified by the data, and can represent many different but high performing models corresponding to different settings of parameters, which is exactly when marginalization will make the biggest difference for both calibration and accuracy. (2) Deep ensembles have been mistaken as competing approaches to Bayesian methods, but can be seen as approximate Bayesian marginalization. (3) The structure of neural networks gives rise to a structured prior in function space, which reflects the inductive biases of neural networks that help them generalize. (4) The observed correlation between parameters in flat regions of the loss and a diversity of solutions that provide good generalization is further conducive to Bayesian marginalization, as flat regions occupy a large volume in a high dimensional space, and each different solution will make a good contribution to a Bayesian model average. (5) Recent practical advances for Bayesian deep learning provide improvements in accuracy and calibration compared to standard training, while retaining scalability.

We access the internalized understanding of trained, deep neural networks to perform Bayesian reasoning on complex tasks. Independently trained networks are arranged to jointly answer questions outside their original scope, which are formulated in terms of a Bayesian inference problem. We solve this approximately with variational inference, which provides uncertainty on the outcomes. We demonstrate how following tasks can be approached this way: Combining independently trained networks to sample from a conditional generator, solving riddles involving multiple constraints simultaneously, and combine deep-learned knowledge with conventional noisy measurements in the context of high-resolution images of human faces.

We analyse perception and memory using mathematical models for knowledge graphs and tensors to gain insights in the corresponding functionalities of the human mind. Our discussion is based on the concept of propositional sentences consisting of \textit{subject-predicate-object} (SPO) triples for expressing elementary facts. SPO sentences are the basis for most natural languages but might also be important for explicit perception and declarative memories, as well as intra-brain communication and the ability to argue and reason. A set of SPO sentences can be described as a knowledge graph, which can be transformed into an adjacency tensor. We introduce tensor models, where concepts have dual representations as indices and associated embeddings, two constructs we believe are essential for the understanding of implicit and explicit perception and memory in the brain. We argue that a biological realization of perception and memory imposes constraints on information processing. In particular, we propose that explicit perception and declarative memories require a semantic decoder, which, in a simple realization, is based on four layers: First, a sensory memory layer, as a buffer for sensory input, second, an index layer representing concepts, third, a memoryless representation layer for the broadcasting of information and fourth, a working memory layer as a processing center and data buffer. In a Bayesian brain interpretation, semantic memory defines the prior for triple statements. We propose that, in evolution and during development, semantic memory, episodic memory and natural language evolved as emergent properties in the agents' process to gain deeper understanding of sensory information. We present a concrete model realization and validate some aspects of our proposed model on benchmark data where we demonstrate state-of-the-art performance.

A great number of computer vision publications have focused on distinguishing between human action recognition and classification rather than the intensity of actions performed. Indexing the intensity which determines the performance of human actions is a challenging task due to the uncertainty and information deficiency that exists in the video inputs. To remedy this uncertainty, in this paper, we coupled fuzzy logic rules with the neural-based action recognition model to index the intensity of the action as intense or mild. In our approach, we define fuzzy logic rules to detect the intensity index of the performed action using the weights generated by the Spatio-Temporal LSTM and demonstrate through experiments that indexing of the action intensity is possible. We analyzed the integrated model by applying it to videos of human actions with different action intensities and were able to achieve an accuracy of 89.16% on our generated dataset for intensity indexing. The integrated model demonstrates the ability of the fuzzy inference module to effectively estimate the intensity index of the human action.

In recent years, there has been an increasing interest in studying causality-related properties in machine learning models generally, and in generative models in particular. While that is well motivated, it inherits the fundamental computational hardness of probabilistic inference, making exact reasoning intractable. Probabilistic tractable models have also recently emerged, which guarantee that conditional marginals can be computed in time linear in the size of the model, where the model is usually learned from data. Although initially limited to low tree-width models, recent tractable models such as sum product networks (SPNs) and probabilistic sentential decision diagrams (PSDDs) exploit efficient function representations and also capture high tree-width models. In this paper, we ask the following technical question: can we use the distributions represented or learned by these models to perform causal queries, such as reasoning about interventions and counterfactuals? By appealing to some existing ideas on transforming such models to Bayesian networks, we answer mostly in the negative. We show that when transforming SPNs to a causal graph interventional reasoning reduces to computing marginal distributions; in other words, only trivial causal reasoning is possible. For PSDDs the situation is only slightly better. We first provide an algorithm for constructing a causal graph from a PSDD, which introduces augmented variables. Intervening on the original variables, once again, reduces to marginal distributions, but when intervening on the augmented variables, a deterministic but nonetheless causal-semantics can be provided for PSDDs.

Conformance checking techniques are widely adopted to pinpoint possible discrepancies between process models and the execution of the process in reality. However, state of the art approaches adopt a crisp evaluation of deviations, with the result that small violations are considered at the same level of significant ones. This affects the quality of the provided diagnostics, especially when there exists some tolerance with respect to reasonably small violations, and hampers the flexibility of the process. In this work, we propose a novel approach which allows to represent actors' tolerance with respect to violations and to account for severity of deviations when assessing executions compliance. We argue that besides improving the quality of the provided diagnostics, allowing some tolerance in deviations assessment also enhances the flexibility of conformance checking techniques and, indirectly, paves the way for improving the resilience of the overall process management system.

The goal of the variational autoencoder (VAE) is to learn a probability distribution $Pr(\mathbf{x})$ over a multi-dimensional variable $\mathbf{x}$. There are two main reasons for modelling distributions. First, we might want to draw samples (generate) from the distribution to create new plausible values of $\mathbf{x}$. Second, we might want to measure the likelihood that a new vector $\mathbf{x} {*}$ was created by this probability distribution. In fact, it turns out that the variational autoencoder is well-suited to the former task but not for the latter. It is common to talk about the variational autoencoder as if it is the model of $Pr(\mathbf{x})$. However, this is misleading; the variational autoencoder is a neural architecture that is designed to help learn the model for $Pr(\mathbf{x})$.