Conditional density estimation is a general framework for solving various problems in machine learning. Among existing methods, non-parametric and/or kernel-based methods are often difficult to use on large datasets, while methods based on neural networks usually make restrictive parametric assumptions on the probability densities. Here, we propose a novel method for estimating the conditional density based on score matching. In contrast to existing methods, we employ scalable neural networks, but do not make explicit parametric assumptions on densities. The key challenge in applying score matching to neural networks is computation of the first- and second-order derivatives of a model for the log-density. We tackle this challenge by developing a new neural-kernelized approach, which can be applied on large datasets with stochastic gradient descent, while the reproducing kernels allow for easy computation of the derivatives needed in score matching. We show that the neural-kernelized function approximator has universal approximation capability and that our method is consistent in conditional density estimation. We numerically demonstrate that our method is useful in high-dimensional conditional density estimation, and compares favourably with existing methods. Finally, we prove that the proposed method has interesting connections to two probabilistically principled frameworks of representation learning: Nonlinear sufficient dimension reduction and nonlinear independent component analysis.

Deep Gaussian processes (DGPs) provide a Bayesian non-parametric alternative to standard parametric deep learning models. A DGP is formed by stacking multiple GPs resulting in a well-regularized composition of functions. The Bayesian framework that equips the model with attractive properties, such as implicit capacity control and predictive uncertainty, makes it at the same time challenging to combine with a convolutional structure. This has hindered the application of DGPs in computer vision tasks, an area where deep parametric models (i.e. CNNs) have made breakthroughs. Standard kernels used in DGPs such as radial basis functions (RBFs) are insufficient for handling pixel variability in raw images. In this paper, we build on the recent convolutional GP to develop Convolutional DGP (CDGP) models which effectively capture image level features through the use of convolution kernels, therefore opening up the way for applying DGPs to computer vision tasks. Our model learns local spatial influence and outperforms strong GP based baselines on multi-class image classification. We also consider various constructions of convolution kernel over the image patches, analyze the computational trade-offs and provide an efficient framework for convolutional DGP models. The experimental results on image data such as MNIST, rectangles-image, CIFAR10 and Caltech101 demonstrate the effectiveness of the proposed approaches.

GuideR: a guided separate-and-conquer rule learning in classification, regression, and survival settings Marek Sikora a,b,, Łukasz Wróbel a,b,, Adam Gudyś a, a Institute of Informatics, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland b Institute of Innovative Technologies, EMAG, Leopolda 31, 40-189 Katowice, PolandAbstract This article presents GuideR, a user-guided rule induction algorithm, which overcomes the largest limitation of the existing methods---the lack of the possibility to introduce user's preferences or domain knowledge to the rule learning process. Automatic selection of attributes and attribute ranges often leads to the situation in which resulting rules do not contain interesting information. We propose an induction algorithm which takes into account user's requirements. Our method uses the sequential covering approach and is suitable for classification, regression, and survival analysis problems. The effectiveness of the algorithm in all these tasks has been verified experimentally, confirming guided rule induction to be a powerful data analysis tool. Introduction Sequential covering rule induction algorithms can be used for both, predictive and descriptive purposes [1, 2, 3, 4]. In spite of the development of increasingly sophisticated versions of those algorithms [5, 6], the main principle remains unchanged and involves two phases: rule growing and rule pruning. In the latter, some of these conditions are removed. In comparison to other machine learning methods, rule sets obtained by sequential covering algorithm, also known as separate-and-conquer strategy (SnC), are characterized by good predictive as well as descriptive capabilities. Taking into consideration only the former, superior results can often be obtained using other methods, e.g. However, data models obtained this way are much less comprehensible than rule sets. In the case of rule learning for descriptive purposes, the algorithms of association rule induction [12, 13, 14] or subgroup discovery [15, 6], are applied. The former leads to a very large number of rules which must then be limited by filtering according to rule interestingness measures [16, 17, 18]. Nevertheless, rule sets obtained by subgroup discovery are characterized by worse predictive abilities than those generated by the standard sequential covering approach. Therefore, if creating a prediction system with comprehensible data model is the main objective, the application of sequential covering rule induction algorithms provides the most sensible solution.

Classifier ensembles are pattern recognition structures composed of a set of classification algorithms (members), organized in a parallel way, and a combination method with the aim of increasing the classification accuracy of a classification system. In this study, we investigate the application of a generalized mixture (GM) functions as a new approach for providing an efficient combination procedure for these systems through the use of dynamic weights in the combination process. Therefore, we present three GM functions to be applied as a combination method. The main advantage of these functions is that they can define dynamic weights at the member outputs, making the combination process more efficient. In order to evaluate the feasibility of the proposed approach, an empirical analysis is conducted, applying classifier ensembles to 25 different classification data sets. In this analysis, we compare the use of the proposed approaches to ensembles using traditional combination methods as well as the state-of-the-art ensemble methods. Our findings indicated gains in terms of performance when comparing the proposed approaches to the traditional ones as well as comparable results with the state-of-the-art methods.

We provide a conceptual map to navigate causal analysis problems. Focusing on the case of discrete random variables, we consider the case of causal effect estimation from observational data. The presented approaches apply also to continuous variables, but the issue of estimation becomes more complex. We then introduce the four schools of thought for causal analysis

We prove that idealised discriminative Bayesian neural networks, capturing perfect epistemic uncertainty, cannot have adversarial examples: Techniques for crafting adversarial examples will necessarily fail to generate perturbed images which fool the classifier. This suggests why MC dropout-based techniques have been observed to be fairly effective against adversarial examples. We support our claims mathematically and empirically. We experiment with HMC on synthetic data derived from MNIST for which we know the ground truth image density, showing that near-perfect epistemic uncertainty correlates to density under image manifold, and that adversarial images lie off the manifold. Using our new-found insights we suggest a new attack for MC dropout-based models by looking for imperfections in uncertainty estimation, and also suggest a mitigation. Lastly, we demonstrate our mitigation on a cats-vs-dogs image classification task with a VGG13 variant.

The era of'big data' offers enormous opportunities for societal improvements. There is an expectation – and even excitement – that, by simply applying sophisticated machine learning algorithms to'big data' sets, we may automatically find solutions to problems that were previously either unsolvable or would incur prohibitive economic costs. Yet, the clever algorithms needed to process big data cannot (and will never) solve most of the critical risk analysis problems that we face. Big data, even when carefully collected is typically unstructured and noisy; even the'biggest data' typically lack crucial, often hidden, information about key causal or explanatory variables that generate or influence the data we observe. For example, the world's leading economists failed to predict the 2008–2010 international financial crisis because they relied on models based on historical statistical data that could not adapt to new circumstances, even when those circumstances were foreseeable by contrarian experts.

Fitness landscape analysis investigates features with a high influence on the performance of optimization algorithms, aiming to take advantage of the addressed problem characteristics. In this work, a fitness landscape analysis using problem features is performed for a Multi-objective Bayesian Optimization Algorithm (mBOA) on instances of MNK-landscape problem for 2, 3, 5 and 8 objectives. We also compare the results of mBOA with those provided by NSGA-III through the analysis of their estimated runtime necessary to identify an approximation of the Pareto front. Moreover, in order to scrutinize the probabilistic graphic model obtained by mBOA, the Pareto front is examined according to a probabilistic view. The fitness landscape study shows that mBOA is moderately or loosely influenced by some problem features, according to a simple and a multiple linear regression model, which is being proposed to predict the algorithms performance in terms of the estimated runtime. Besides, we conclude that the analysis of the probabilistic graphic model produced at the end of evolution can be useful to understand the convergence and diversity performances of the proposed approach.

Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules to imprecise-probabilistic uncertainty models. We provide them with a clear interpretation in terms of attitudes towards gambling, borrowing ideas from the theory of sets of desirable gambles, and we use this interpretation to derive a set of basic axioms. We show that these axioms lead to a full-fledged theory of coherent choice functions, which includes a representation in terms of sets of desirable gambles, and a conservative inference method.

We consider a network scenario in which agents can evaluate each other according to a score graph that models some interactions. The goal is to design a distributed protocol, run by the agents, that allows them to learn their unknown state among a finite set of possible values. We propose a Bayesian framework in which scores and states are associated to probabilistic events with unknown parameters and hyperparameters, respectively. We show that each agent can learn its state by means of a local Bayesian classifier and a (centralized) Maximum-Likelihood (ML) estimator of parameter-hyperparameter that combines plain ML and Empirical Bayes approaches. By using tools from graphical models, which allow us to gain insight on conditional dependencies of scores and states, we provide a relaxed probabilistic model that ultimately leads to a parameter-hyperparameter estimator amenable to distributed computation. To highlight the appropriateness of the proposed relaxation, we demonstrate the distributed estimators on a social interaction setup for user profiling. A common feature of online social networks (OSNs) is the possibility of individuals to continuously interact among themselves, by sharing contents and expressing opinions or ratings on different topics [1], [2].