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.

Time series data is a collection of chronological observations which is generated by several domains such as medical and financial fields. Over the years, different tasks such as classification, forecasting, and clustering have been proposed to analyze this type of data. Time series data has been also used to study the effect of interventions over time. Moreover, in many fields of science, learning the causal structure of dynamic systems and time series data is considered an interesting task which plays an important role in scientific discoveries. Estimating the effect of an intervention and identifying the causal relations from the data can be performed via causal inference. Existing surveys on time series discuss traditional tasks such as classification and forecasting or explain the details of the approaches proposed to solve a specific task. In this paper, we focus on two causal inference tasks, i.e., treatment effect estimation and causal discovery for time series data, and provide a comprehensive review of the approaches in each task. Furthermore, we curate a list of commonly used evaluation metrics and datasets for each task and provide in-depth insight. These metrics and datasets can serve as benchmarks for research in the field.

We present a new CUSUM procedure for sequentially detecting change-point in the self and mutual exciting processes, a.k.a. Hawkes networks using discrete events data. Hawkes networks have become a popular model for statistics and machine learning due to their capability in modeling irregularly observed data where the timing between events carries a lot of information. The problem of detecting abrupt changes in Hawkes networks arises from various applications, including neuronal imaging, sensor network, and social network monitoring. Despite this, there has not been a computationally and memory-efficient online algorithm for detecting such changes from sequential data. We present an efficient online recursive implementation of the CUSUM statistic for Hawkes processes, both decentralized and memory-efficient, and establish the theoretical properties of this new CUSUM procedure. We then show that the proposed CUSUM method achieves better performance than existing methods, including the Shewhart procedure based on count data, the generalized likelihood ratio (GLR) in the existing literature, and the standard score statistic. We demonstrate this via a simulated example and an application to population code change-detection in neuronal networks.

The automation of probabilistic reasoning is one of the primary aims of machine learning. Recently, the confluence of variational inference and deep learning has led to powerful and flexible automatic inference methods that can be trained by stochastic gradient descent. In particular, normalizing flows are highly parameterized deep models that can fit arbitrarily complex posterior densities. However, normalizing flows struggle in highly structured probabilistic programs as they need to relearn the forward-pass of the program. Automatic structured variational inference (ASVI) remedies this problem by constructing variational programs that embed the forward-pass. Here, we combine the flexibility of normalizing flows and the prior-embedding property of ASVI in a new family of variational programs, which we named cascading flows. A cascading flows program interposes a newly designed highway flow architecture in between the conditional distributions of the prior program such as to steer it toward the observed data. These programs can be constructed automatically from an input probabilistic program and can also be amortized automatically. We evaluate the performance of the new variational programs in a series of structured inference problems. We find that cascading flows have much higher performance than both normalizing flows and ASVI in a large set of structured inference problems.

This graduate textbook on machine learning tells a story of how patterns in data support predictions and consequential actions. Starting with the foundations of decision making, we cover representation, optimization, and generalization as the constituents of supervised learning. A chapter on datasets as benchmarks examines their histories and scientific bases. Self-contained introductions to causality, the practice of causal inference, sequential decision making, and reinforcement learning equip the reader with concepts and tools to reason about actions and their consequences. Throughout, the text discusses historical context and societal impact. We invite readers from all backgrounds; some experience with probability, calculus, and linear algebra suffices.

Exploration in unknown environments is a fundamental problem in reinforcement learning and control. In this work, we study task-guided exploration and determine what precisely an agent must learn about their environment in order to complete a particular task. Formally, we study a broad class of decision-making problems in the setting of linear dynamical systems, a class that includes the linear quadratic regulator problem. We provide instance- and task-dependent lower bounds which explicitly quantify the difficulty of completing a task of interest. Motivated by our lower bound, we propose a computationally efficient experiment-design based exploration algorithm. We show that it optimally explores the environment, collecting precisely the information needed to complete the task, and provide finite-time bounds guaranteeing that it achieves the instance- and task-optimal sample complexity, up to constant factors. Through several examples of the LQR problem, we show that performing task-guided exploration provably improves on exploration schemes which do not take into account the task of interest. Along the way, we establish that certainty equivalence decision making is instance- and task-optimal, and obtain the first algorithm for the linear quadratic regulator problem which is instance-optimal. We conclude with several experiments illustrating the effectiveness of our approach in practice.