Evidence in probabilistic reasoning may be ‘hard’ or ‘soft’, that is, it may be of yes/no form, or it may involve a strength of belief, in the unit interval [0, 1]. Reasoning with soft, [0, 1]-valued evidence is important in many situations but may lead to different, confusing interpretations. This paper intends to bring more mathematical and conceptual clarity to the field by shifting the existing focus from specification of soft evidence to accomodation of soft evidence. There are two main approaches, known as Jeffrey’s rule and Pearl’s method; they give different outcomes on soft evidence. This paper argues that they can be understood as correction and as improvement. It describes these two approaches as different ways of updating with soft evidence, highlighting their differences, similarities and applications. This account is based on a novel channel-based approach to Bayesian probability. Proper understanding of these two update mechanisms is highly relevant for inference, decision tools and probabilistic programming languages.

Deep neural network (DNN) regression models are widely used in applications requiring state-of-the-art predictive accuracy. However, until recently there has been little work on accurate uncertainty quantification for predictions from such models. We add to this literature by outlining an approach to constructing predictive distributions that are `marginally calibrated'. This is where the long run average of the predictive distributions of the response variable matches the observed empirical margin. Our approach considers a DNN regression with a conditionally Gaussian prior for the final layer weights, from which an implicit copula process on the feature space is extracted. This copula process is combined with a non-parametrically estimated marginal distribution for the response. The end result is a scalable distributional DNN regression method with marginally calibrated predictions, and our work complements existing methods for probability calibration. The approach is first illustrated using two applications of dense layer feed-forward neural networks. However, our main motivating applications are in likelihood-free inference, where distributional deep regression is used to estimate marginal posterior distributions. In two complex ecological time series examples we employ the implicit copulas of convolutional networks, and show that marginal calibration results in improved uncertainty quantification. Our approach also avoids the need for manual specification of summary statistics, a requirement that is burdensome for users and typical of competing likelihood-free inference methods.

Due to the popularity of context-awareness in the Internet of Things (IoT) and the recent advanced features in the most popular IoT device, i.e., smartphone, modeling and predicting personalized usage behavior based on relevant contexts can be highly useful in assisting them to carry out daily routines and activities. Usage patterns of different categories smartphone apps such as social networking, communication, entertainment, or daily life services related apps usually vary greatly between individuals. People use these apps differently in different contexts, such as temporal context, spatial context, individual mood and preference, work status, Internet connectivity like Wifi? status, or device related status like phone profile, battery level etc. Thus, we consider individuals' apps usage as a multi-class context-aware problem for personalized modeling and prediction. Random Forest learning is one of the most popular machine learning techniques to build a multi-class prediction model. Therefore, in this paper, we present an effective context-aware smartphone apps prediction model, and name it "AppsPred" using random forest machine learning technique that takes into account optimal number of trees based on such multi-dimensional contexts to build the resultant forest. The effectiveness of this model is examined by conducting experiments on smartphone apps usage datasets collected from individual users. The experimental results show that our AppsPred significantly outperforms other popular machine learning classification approaches like ZeroR, Naive Bayes, Decision Tree, Support Vector Machines, Logistic Regression while predicting smartphone apps in various context-aware test cases.

Many learning algorithms require categorical data to be transformed into real vectors before it can be used as input. Often, categorical variables are encoded as one-hot (or dummy) vectors. However, this mode of representation can be wasteful since it adds many low-signal regressors, especially when the number of unique categories is large. In this paper, we investigate simple alternative solutions for universally consistent estimators that rely on lower-dimensional real-valued representations of categorical variables that are "sufficient" in the sense that no predictive information is lost. We then compare preexisting and proposed methods on simulated and observational datasets.

Ecologists have long suspected that species are more likely to interact if their traits match in a particular way. For example, a pollination interaction may be particularly likely if the proportions of a bee's tongue match flower shape in a beneficial way. Empirical evidence for trait matching, however, varies significantly in strength among different types of ecological networks. Here, we show that ambiguity among empirical trait matching studies may have arisen at least in parts from using overly simple statistical models. Using simulated and real data, we contrast conventional regression models with Machine Learning (ML) models (Random Forest, Boosted Regression Trees, Deep Neural Networks, Convolutional Neural Networks, Support Vector Machines, naive Bayes, and k-Nearest-Neighbor), testing their ability to predict species interactions based on traits, and infer trait combinations causally responsible for species interactions. We find that the best ML models can successfully predict species interactions in plant-pollinator networks (up to 0.93 AUC) and outperform conventional regression models. Our results also demonstrate that ML models can better identify the causally responsible trait matching combinations than GLMs. In two case studies, the best ML models could successfully predict species interactions in a global plant-pollinator database and infer ecologically plausible trait matching rules for a plant-hummingbird network from Costa Rica, without any prior assumptions about the system. We conclude that flexible ML models offer many advantages over traditional regression models for understanding interaction networks. We anticipate that these results extrapolate to other network types, such as trophic or competitive networks. More generally, our results highlight the potential of ML and artificial intelligence for inference beyond standard tasks such as pattern recognition.

In this work, we introduce a novel probabilistic representation of deep learning, which provides an explicit explanation for the Deep Neural Networks (DNNs) in three aspects: (i) neurons define the energy of a Gibbs distribution; (ii) the hidden layers of DNNs formulate Gibbs distributions; and (iii) the whole architecture of DNNs can be interpreted as a Bayesian neural network. Based on the proposed probabilistic representation, we investigate two fundamental properties of deep learning: hierarchy and generalization. First, we explicitly formulate the hierarchy property from the Bayesian perspective, namely that some hidden layers formulate a prior distribution and the remaining layers formulate a likelihood distribution. Second, we demonstrate that DNNs have an explicit regularization by learning a prior distribution and the learning algorithm is one reason for decreasing the generalization ability of DNNs. Moreover, we clarify two empirical phenomena of DNNs that cannot be explained by traditional theories of generalization. Simulation results validate the proposed probabilistic representation and the insights into these properties of deep learning based on a synthetic dataset.

We present an analysis of predictive uncertainty based out-of-distribution detection for different approaches to estimate various models' epistemic uncertainty and contrast it with extreme value theory based open set recognition. While the former alone does not seem to be enough to overcome this challenge, we demonstrate that uncertainty goes hand in hand with the latter method. This seems to be particularly reflected in a generative model approach, where we show that posterior based open set recognition outperforms discriminative models and predictive uncertainty based outlier rejection, raising the question of whether classifiers need to be generative in order to know what they have not seen.

Semi-supervised learning is a setting in which one has labeled and unlabeled data available. In this survey we explore different types of theoretical results when one uses unlabeled data in classification and regression tasks. Most methods that use unlabeled data rely on certain assumptions about the data distribution. When those assumptions are not met in reality, including unlabeled data may actually decrease performance. Studying such methods, it therefore is particularly important to have an understanding of the underlying theory. In this review we gather results about the possible gains one can achieve when using semi-supervised learning as well as results about the limits of such methods. More precisely, this review collects the answers to the following questions: What are, in terms of improving supervised methods, the limits of semi-supervised learning? What are the assumptions of different methods? What can we achieve if the assumptions are true? Finally, we also discuss the biggest bottleneck of semi-supervised learning, namely the assumptions they make.

Normalizing Flows are generative models which produce tractable distributions where both sampling and density evaluation can be efficient and exact. The goal of this survey article is to give a coherent and comprehensive review of the literature around the construction and use of Normalizing Flows for distribution learning. We aim to provide context and explanation of the models, review current state-of-the-art literature, and identify open questions and promising future directions.