The goal of this paper is to explore the basic Approximate Bayesian Computation (ABC) algorithm via the lens of information theory. ABC is a widely used algorithm in cases where the likelihood of the data is hard to work with or intractable, but one can simulate from it. We use relative entropy ideas to analyze the behavior of the algorithm as a function of the thresholding parameter and of the size of the data. Relative entropy here is data driven as it depends on the values of the observed statistics. We allow different thresholding parameters for each different direction (i.e. for different observed statistic) and compute the weighted effect on each direction. The latter allows to find important directions via sensitivity analysis leading to potentially larger acceptance regions, which in turn brings the computational cost of the algorithm down for the same level of accuracy. In addition, we also investigate the bias of the estimators for generic observables as a function of both the thresholding parameters and the size of the data. Our analysis provides error bounds on performance for positive tolerances and finite sample sizes. Simulation studies complement and illustrate the theoretical results.

Online crowdsourcing provides a scalable and inexpensive means to collect knowledge (e.g. labels) about various types of data items (e.g. text, audio, video). However, it is also known to result in large variance in the quality of recorded responses which often cannot be directly used for training machine learning systems. To resolve this issue, a lot of work has been conducted to control the response quality such that low-quality responses cannot adversely affect the performance of the machine learning systems. Such work is referred to as the quality control for crowdsourcing. Past quality control research can be divided into two major branches: quality control mechanism design and statistical models. The first branch focuses on designing measures, thresholds, interfaces and workflows for payment, gamification, question assignment and other mechanisms that influence workers' behaviour. The second branch focuses on developing statistical models to perform effective aggregation of responses to infer correct responses. The two branches are connected as statistical models (i) provide parameter estimates to support the measure and threshold calculation, and (ii) encode modelling assumptions used to derive (theoretical) performance guarantees for the mechanisms. There are surveys regarding each branch but they lack technical details about the other branch. Our survey is the first to bridge the two branches by providing technical details on how they work together under frameworks that systematically unify crowdsourcing aspects modelled by both of them to determine the response quality. We are also the first to provide taxonomies of quality control papers based on the proposed frameworks. Finally, we specify the current limitations and the corresponding future directions for the quality control research.

Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling them. While there are many methods for modeling nonlinear dynamical systems, existing techniques face a trade off between offering interpretable descriptions and making accurate predictions. Here, we develop a class of models that aims to achieve both simultaneously, smoothly interpolating between simple descriptions and more complex, yet also more accurate models. Our probabilistic model achieves this multi-scale property through a hierarchy of locally linear dynamics that jointly approximate global nonlinear dynamics. We call it the tree-structured recurrent switching linear dynamical system. To fit this model, we present a fully-Bayesian sampling procedure using Polya-Gamma data augmentation to allow for fast and conjugate Gibbs sampling. Through a variety of synthetic and real examples, we show how these models outperform existing methods in both interpretability and predictive capability.

FRAME (Filters, Random fields, And Maximum Entropy) is an energy-based descriptive model that synthesizes visual realism by capturing mutual patterns from structural input signals. The maximum likelihood estimation (MLE) is applied by default, yet conventionally causes the unstable training energy that wrecks the generated structures, which remains unexplained. In this paper, we provide a new theoretical insight to analyze FRAME, from a perspective of particle physics ascribing the weird phenomenon to KL-vanishing issue. In order to stabilize the energy dissipation, we propose an alternative Wasserstein distance in discrete time based on the conclusion that the Jordan-Kinderlehrer-Otto (JKO) discrete flow approximates KL discrete flow when the time step size tends to 0. Besides, this metric can still maintain the model's statistical consistency. Quantitative and qualitative experiments have been respectively conducted on several widely used datasets. The empirical studies have evidenced the effectiveness and superiority of our method.

We introduce a genetic algorithm that designs quantum optics experiments for engineering quantum states with specific properties. Our algorithm is powerful and flexible, and can easily be modified to find methods of engineering states for a range of applications. Here we focus on quantum metrology. First, we consider the noise-free case, and use the algorithm to find quantum states with a large quantum Fisher information (QFI). We find methods, which only involve experimental elements that are available with current technology, for engineering quantum states with up to a 100-fold improvement over the best classical state, and a 20-fold improvement over the optimal Gaussian state. Such states are a superposition of the vacuum with a large number of photons (around 80), and can hence be seen as Schr\"odinger-cat-like states. We then apply the two most dominant noise sources in our setting -- photon loss and imperfect heralding -- and use the algorithm to find quantum states that still improve over the optimal Gaussian state with realistic levels of noise. This will open up experimental and technological work in using exotic non-Gaussian states for quantum-enhanced phase measurements. Finally, we use the Bayesian mean square error to look beyond the regime of validity of the QFI, finding quantum states with precision enhancements over the alternatives even when the experiment operates in the regime of limited data.

The ability for autonomous agents to learn and conform to human norms is crucial for their safety and effectiveness in social environments. While recent work has led to frameworks for the representation and inference of simple social rules, research into norm learning remains at an exploratory stage. Here, we present a robotic system capable of representing, learning, and inferring ownership relations and norms. Ownership is represented as a graph of probabilistic relations between objects and their owners, along with a database of predicate-based norms that constrain the actions permissible on owned objects. To learn these norms and relations, our system integrates (i) a novel incremental norm learning algorithm capable of both one-shot learning and induction from specific examples, (ii) Bayesian inference of ownership relations in response to apparent rule violations, and (iii) percept-based prediction of an object's likely owners. Through a series of simulated and real-world experiments, we demonstrate the competence and flexibility of the system in performing object manipulation tasks that require a variety of norms to be followed, laying the groundwork for future research into the acquisition and application of social norms.

Recently, compression and acceleration of deep neural networks are in critic need. Bayesian generalization of structured pruning represents an important research direction to solve the above problem. However, the existing Bayesian methods ignore the dependency among neurons and filters for computational simplicity. In this study, we explore, under Bayesian framework, a structured pruning method with layer-wise sequential dependency assumed, a more general learning setting. Based on the property of Dirac distribution, we further derive a new dropout noise, which makes it possible to approximate the posterior of dropout noise knowing that of the previous layer. With the Dirac-like dropout noise, we further propose a recursive strategy, named \emph{Recursive Bayesian Pruning} (RBP), to train and prune networks in a layer-by-layer fashion. The unimportant neurons and filters are directly targeted and removed, taking the influence from the previous layer. Experiments on typical neural networks LeNet-300-100, LeNet-5 and VGG-16 have demonstrated the proposed method are competitive with or even outperform the state-of-the-art methods in several compression and acceleration metrics.

Labeling training data is one of the most costly bottlenecks in developing or modifying machine learning-based applications. We survey how resources from across an organization can be used as weak supervision sources for three classification tasks at Google, in order to bring development time and cost down by an order of magnitude. We build on the Snorkel framework, extending it as a new system, Snorkel DryBell, which integrates with Google's distributed production systems and enables engineers to develop and execute weak supervision strategies over millions of examples in less than thirty minutes. We find that Snorkel DryBell creates classifiers of comparable quality to ones trained using up to tens of thousands of hand-labeled examples, in part by leveraging organizational resources not servable in production which contribute an average 52% performance improvement to the weakly supervised classifiers.

The ability to learn and act in novel situations is still a prerogative of animate intelligence, as current machine learning methods mostly fail when moving beyond the standard i.i.d. setting. What is the reason for this discrepancy? Most machine learning tasks are anti-causal, i.e., we infer causes (labels) from effects (observations). Typically, in supervised learning we build systems that try to directly invert causal mechanisms. Instead, in this paper we argue that strong generalization capabilities crucially hinge on searching and validating meaningful hypotheses, requiring access to a causal model. In such a framework, we want to find a cause that leads to the observed effect. Anti-causal models are used to drive this search, but a causal model is required for validation. We investigate the fundamental differences between causal and anti-causal tasks, discuss implications for topics ranging from adversarial attacks to disentangling factors of variation, and provide extensive evidence from the literature to substantiate our view. We advocate for incorporating causal models in supervised learning to shift the paradigm from inference only, to search and validation.

Expectation maximization (EM) algorithm is to find maximum likelihood solution for models having latent variables. A typical example is Gaussian Mixture Model (GMM) which requires Gaussian assumption, however, natural images are highly non-Gaussian so that GMM cannot be applied to perform clustering task on pixel space. To overcome such limitation, we propose a GAN based EM learning framework that can maximize the likelihood of images and estimate the latent variables with only the constraint of L-Lipschitz continuity. We call this model GAN-EM, which is a framework for image clustering, semi-supervised classification and dimensionality reduction. In M-step, we design a novel loss function for discriminator of GAN to perform maximum likelihood estimation (MLE) on data with soft class label assignments. Specifically, a conditional generator captures data distribution for $K$ classes, and a discriminator tells whether a sample is real or fake for each class. Since our model is unsupervised, the class label of real data is regarded as latent variable, which is estimated by an additional network (E-net) in E-step. The proposed GAN-EM achieves state-of-the-art clustering and semi-supervised classification results on MNIST, SVHN and CelebA, as well as comparable quality of generated images to other recently developed generative models.