This paper reports a novel method for supervised machine learning based on the mathematical formalism that supports quantum mechanics. The method uses projective quantum measurement as a way of building a prediction function. Specifically, the relationship between input and output variables is represented as the state of a bipartite quantum system. The state is estimated from training samples through an averaging process that produces a density matrix. Prediction of the label for a new sample is made by performing a projective measurement on the bipartite system with an operator, prepared from the new input sample, and applying a partial trace to obtain the state of the subsystem representing the output. The method can be seen as a generalization of Bayesian inference classification and as a type of kernel-based learning method. One remarkable characteristic of the method is that it does not require learning any parameters through optimization. We illustrate the method with different 2-D classification benchmark problems and different quantum information encodings.

Inferring the parameters of a stochastic model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e., when distinct sets of parameters yield identical observations. This arises in many practical situations, such as when inferring the distance and power of a radio source (is the source close and weak or far and strong?) or when estimating the amplifier gain and underlying brain activity of an electrophysiological experiment. In this work, we present a method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters. Our method extends recent developments in simulation-based inference(SBI) based on normalizing flows to Bayesian hierarchical models. We validate quantitatively our proposal on a motivating example amenable to analytical solutions, and then apply it to invert a well known non-linear model from computational neuroscience.

Riemannian manifolds provide a principled way to model nonlinear geometric structure inherent in data. A Riemannian metric on said manifolds determines geometry-aware shortest paths and provides the means to define statistical models accordingly. However, these operations are typically computationally demanding. To ease this computational burden, we advocate probabilistic numerical methods for Riemannian statistics. In particular, we focus on Bayesian quadrature (BQ) to numerically compute integrals over normal laws on Riemannian manifolds learned from data. In this task, each function evaluation relies on the solution of an expensive initial value problem. We show that by leveraging both prior knowledge and an active exploration scheme, BQ significantly reduces the number of required evaluations and thus outperforms Monte Carlo methods on a wide range of integration problems. As a concrete application, we highlight the merits of adopting Riemannian geometry with our proposed framework on a nonlinear dataset from molecular dynamics.

In a Bayesian neural network (BNN), we specify a prior p(w) over the neural network parameters, and compute the posterior distribution over parameters conditioned on training data, p(w x, y) p(y w, x)p(w)/p(y x). This procedure should give considerable advantages for reasoning about predictive uncertainty, which is especially relevant in the small-data setting. Crucially, to perform Bayesian inference, we need to choose a prior that accurately reflects our beliefs about the parameters before seeing any data (Bayes, 1763; Gelman et al., 2013). However, the most common choice of the prior for BNN weights is the simplest one: the isotropic Gaussian. Isotropic Gaussians are used across almost all fields of Bayesian deep learning, ranging from variational inference (Blundell et al., 2015; Dusenberry et al., 2020), to sampling-based inference (Zhang et al., 2019), and even to infinite networks (Lee et al., 2017; Garriga-Alonso et al., 2019). This is troubling, since isotropic Gaussian priors are almost certainly not the best choice. Indeed, despite the progress on more accurate and efficient inference procedures, in most settings, the posterior predictive of BNNs using a Gaussian prior still leads to worse predictive performance than a baseline obtained by training the network with standard stochastic gradient descent (SGD) (e.g., Zhang et al., 2019; Heek & Kalchbrenner, 2019; Wenzel et al., 2020a). However, it has been shown that the performance of BNNs can be improved by artificially reducing posterior uncertainty using "cold posteriors" (Wenzel et al., 2020a).

The family of methods collectively known as classifier chains has become a popular approach to multi-label learning problems. This approach involves chaining together off-the-shelf binary classifiers in a directed structure, such that individual label predictions become features for other classifiers. Such methods have proved flexible and effective and have obtained state-of-the-art empirical performance across many datasets and multi-label evaluation metrics. This performance led to further studies of the underlying mechanism and efficacy, and investigation into how it could be improved. In the recent decade, numerous studies have explored the theoretical underpinnings of classifier chains, and many improvements have been made to the training and inference procedures, such that this method remains among the best options for multi-label learning. Given this past and ongoing interest, which covers a broad range of applications and research themes, the goal of this work is to provide a review of classifier chains, a survey of the techniques and extensions provided in the literature, as well as perspectives for this approach in the domain of multi-label classification in the future. We conclude positively, with a number of recommendations for researchers and practitioners, as well as outlining key issues for future research.

Mini-batch optimal transport (m-OT) has been successfully used in practical applications that involve probability measures with intractable density, or probability measures with a very high number of supports. The m-OT solves several sparser optimal transport problems and then returns the average of their costs and transportation plans. Despite its scalability advantage, m-OT is not a proper metric between probability measures since it does not satisfy the identity property. To address this problem, we propose a novel mini-batching scheme for optimal transport, named Batch of Mini-batches Optimal Transport (BoMb-OT), that can be formulated as a well-defined distance on the space of probability measures. Furthermore, we show that the m-OT is a limit of the entropic regularized version of the proposed BoMb-OT when the regularized parameter goes to infinity. We carry out extensive experiments to show that the new mini-batching scheme can estimate a better transportation plan between two original measures than m-OT. It leads to a favorable performance of BoMb-OT in the matching and color transfer tasks. Furthermore, we observe that BoMb-OT also provides a better objective loss than m-OT for doing approximate Bayesian computation, estimating parameters of interest in parametric generative models, and learning non-parametric generative models with gradient flow.

Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine learning -- from computing the expectations of decision tree ensembles to information-theoretic divergences of deep mixture models -- can be represented in terms of tractable modular operations over circuits. Specifically, we characterize the tractability of a vocabulary of simple transformations -- sums, products, quotients, powers, logarithms, and exponentials -- in terms of sufficient structural constraints of the circuits they operate on, and present novel hardness results for the cases in which these properties are not satisfied. Building on these operations, we derive a unified framework for reasoning about tractable models that generalizes several results in the literature and opens up novel tractable inference scenarios.

Abstract--Real-world applications have been dealing with large amounts of data that arrive over time and generally present changes in their underlying joint probability distribution, i.e., concept drift. Concept drift can be subdivided into two types: virtual drift, which affects the unconditional probability distribution p(x), and real drift, which affects the conditional probability distribution p(y x) . Existing works focuses on real drift. However, strategies to cope with real drift may not be the best suited for dealing with virtual drift, since the real class boundaries remain unchanged. We provide the first in depth analysis of the differences between the impact of virtual and real drifts on classifiers' suitability. We propose an approach to handle both drifts called On-line Gaussian Mixture Model With Noise Filter For Handling Virtual and Real Concept Drifts (OGMMF-VRD). Experiments with 7 synthetic and 3 real-world datasets show that OGMMF-VRD obtained the best results in terms of average accuracy, G-mean and runtime compared to existing approaches. Moreover, its accuracy over time suffered less performance degradation in the presence of drifts. In recent years, real-world applications like credit card learned decision boundaries, which need to be adjusted for fraud detection, flight delay and weather forecasting have the classifier to remain suitable. Such sequences of data are known as data stream learning approaches treat virtual drifts using data streams [2, 3]. They are challenging for data modeling the same strategies as for real drifts [6].

Modern Code Review (MCR) is the process of reviewing new code changes that need to be merged with an existing codebase. As a developer, one may receive many code review requests every day, i.e., the review requests need to be prioritised. Manually prioritising review requests is a challenging and time-consuming process. To address the above problem, we conducted an industrial case study at Ericsson aiming at developing a tool called Pineapple, which uses a Bayesian Network to prioritise code review requests. To validate our approach/tool, we deployed it in a live software development project at Ericsson, wherein more than 150 developers develop a telecommunication product. We focused on evaluating the predictive performance, feasibility, and usefulness of our approach. The results indicate that Pineapple has competent predictive performance (RMSE = 0.21 and MAE = 0.15). Furthermore, around 82.6% of Pineapple's users believe the tool can support code review request prioritisation by providing reliable results, and around 56.5% of the users believe it helps reducing code review lead time. As future work, we plan to evaluate Pineapple's predictive performance, usefulness, and feasibility through a longitudinal investigation.

Estimation of spatially-varying parameters for computationally expensive forward models governed by partial differential equations is addressed. A novel multiscale Bayesian inference approach is introduced based on deep probabilistic generative models. Such generative models provide a flexible representation by inferring on each scale a low-dimensional latent encoding while allowing hierarchical parameter generation from coarse- to fine-scales. Combining the multiscale generative model with Markov Chain Monte Carlo (MCMC), inference across scales is achieved enabling us to efficiently obtain posterior parameter samples at various scales. The estimation of coarse-scale parameters using a low-dimensional latent embedding captures global and notable parameter features using an inexpensive but inaccurate solver. MCMC sampling of the fine-scale parameters is enabled by utilizing the posterior information in the immediate coarser-scale. In this way, the global features are identified in the coarse-scale with inference of low-dimensional variables and inexpensive forward computation, and the local features are refined and corrected in the fine-scale. The developed method is demonstrated with two types of permeability estimation for flow in heterogeneous media. One is a Gaussian random field (GRF) with uncertain length scales, and the other is channelized permeability with the two regions defined by different GRFs. The obtained results indicate that the method allows high-dimensional parameter estimation while exhibiting stability, efficiency and accuracy.