We consider two questions at the heart of machine learning; how can we predict if a minimum will generalize to the test set, and why does stochastic gradient descent find minima that generalize well? Our work responds to Zhang et al. (2016), who showed deep neural networks can easily memorize randomly labeled training data, despite generalizing well on real labels of the same inputs. We show that the same phenomenon occurs in small linear models. These observations are explained by the Bayesian evidence, which penalizes sharp minima but is invariant to model parameterization. We also demonstrate that, when one holds the learning rate fixed, there is an optimum batch size which maximizes the test set accuracy. We propose that the noise introduced by small mini-batches drives the parameters towards minima whose evidence is large. Interpreting stochastic gradient descent as a stochastic differential equation, we identify the "noise scale" $g = \epsilon (\frac{N}{B} - 1) \approx \epsilon N/B$, where $\epsilon$ is the learning rate, $N$ the training set size and $B$ the batch size. Consequently the optimum batch size is proportional to both the learning rate and the size of the training set, $B_{opt} \propto \epsilon N$. We verify these predictions empirically.

Learning from expert demonstrations has received a lot of attention in artificial intelligence and machine learning. The goal is to infer the underlying reward function that an agent is optimizing given a set of observations of the agent's behavior over time in a variety of circumstances, the system state trajectories, and a plant model specifying the evolution of the system state for different agent's actions. The system is often modeled as a Markov decision process, that is, the next state depends only on the current state and agent's action, and the the agent's choice of action depends only on the current state. While the former is a Markovian assumption on the evolution of system state, the later assumes that the target reward function is itself Markovian. In this work, we explore learning a class of non-Markovian reward functions, known in the formal methods literature as specifications. These specifications offer better composition, transferability, and interpretability. We then show that inferring the specification can be done efficiently without unrolling the transition system. We demonstrate on a 2-d grid world example.

During their first years of life, infants learn the language(s) of their environment at an amazing speed despite large cross cultural variations in amount and complexity of the available language input. Understanding this simple fact still escapes current cognitive and linguistic theories. Recently, spectacular progress in the engineering science, notably, machine learning and wearable technology, offer the promise of revolutionizing the study of cognitive development. Machine learning offers powerful learning algorithms that can achieve human-like performance on many linguistic tasks. Wearable sensors can capture vast amounts of data, which enable the reconstruction of the sensory experience of infants in their natural environment. The project of 'reverse engineering' language development, i.e., of building an effective system that mimics infant's achievements appears therefore to be within reach. Here, we analyze the conditions under which such a project can contribute to our scientific understanding of early language development. We argue that instead of defining a sub-problem or simplifying the data, computational models should address the full complexity of the learning situation, and take as input the raw sensory signals available to infants. This implies that (1) accessible but privacy-preserving repositories of home data be setup and widely shared, and (2) models be evaluated at different linguistic levels through a benchmark of psycholinguist tests that can be passed by machines and humans alike, (3) linguistically and psychologically plausible learning architectures be scaled up to real data using probabilistic/optimization principles from machine learning. We discuss the feasibility of this approach and present preliminary results.

Two fundamental problems in unsupervised learning are efficient inference for latent-variable models and robust density estimation based on large amounts of unlabeled data. Algorithms for the two tasks, such as normalizing flows and generative adversarial networks (GANs), are often developed independently. In this paper, we propose the concept of {\em continuous-time flows} (CTFs), a family of diffusion-based methods that are able to asymptotically approach a target distribution. Distinct from normalizing flows and GANs, CTFs can be adopted to achieve the above two goals in one framework, with theoretical guarantees. Our framework includes distilling knowledge from a CTF for efficient inference, and learning an explicit energy-based distribution with CTFs for density estimation. Both tasks rely on a new technique for distribution matching within amortized learning. Experiments on various tasks demonstrate promising performance of the proposed CTF framework, compared to related techniques.

Training of discrete latent variable models remains challenging because passing gradient information through discrete units is difficult. We propose a new class of smoothing transformations based on a mixture of two overlapping distributions, and show that the proposed transformation can be used for training binary latent models with either directed or undirected priors. We derive a new variational bound to efficiently train with Boltzmann machine priors. Using this bound, we develop DVAE++, a generative model with a global discrete prior and a hierarchy of convolutional continuous variables. Experiments on several benchmarks show that overlapping transformations outperform other recent continuous relaxations of discrete latent variables including Gumbel-Softmax (Maddison et al., 2016; Jang et al., 2016), and discrete variational autoencoders (Rolfe 2016).

Quadrature is the problem of estimating intractable integrals, a problem that arises in many Bayesian machine learning settings. We present an improved Bayesian framework for estimating intractable integrals of specific kinds of constrained integrands. We derive the necessary approximation scheme for a specific and especially useful instantiation of this framework: the use of a log transformation to model non-negative integrands. We also propose a novel method for optimizing the hyperparameters associated with this framework; we optimize the hyperparameters in the original space of the integrand as opposed to in the transformed space, resulting in a model that better explains the actual data. Experiments on both synthetic and real-world data demonstrate that the proposed framework achieves more-accurate estimates using less wall-clock time than previously preposed Bayesian quadrature procedures for non-negative integrands.

Learning algorithms that aggregate predictions from an ensemble of diverse base classifiers consistently outperform individual methods. Many of these strategies have been developed in a supervised setting, where the accuracy of each base classifier can be empirically measured and this information is incorporated in the training process. However, the reliance on labeled data precludes the application of ensemble methods to many real world problems where labeled data has not been curated. To this end we developed a new theoretical framework for binary classification, the Strategy for Unsupervised Multiple Method Aggregation (SUMMA), to estimate the performances of base classifiers and an optimal strategy for ensemble learning from unlabeled data.

In meta-learning an agent extracts knowledge from observed tasks, aiming to facilitate learning of novel future tasks. Under the assumption that future tasks are 'related' to previous tasks, representations should be learned in a way which captures the common structure across learned tasks, while allowing the learner sufficient flexibility to adapt to novel aspects of new tasks. We present a framework for meta-learning that is based on generalization error bounds, allowing us to extend various PAC-Bayes bounds to meta-learning. Learning takes place through the construction of a distribution over hypotheses based on the observed tasks, and its utilization for learning a new task. Thus, prior knowledge is incorporated through setting an experience-dependent prior for novel tasks. We develop a gradient-based algorithm which minimizes an objective function derived from the bounds and demonstrate its effectiveness numerically with deep neural networks. In addition to establishing the improved performance available through meta-learning, we demonstrate the intuitive way by which prior information is manifested at different levels of the network.

Recent work in unsupervised representation learning has focused on learning deep directed latent-variable models. Fitting these models by maximizing the marginal likelihood or evidence is typically intractable, thus a common approximation is to maximize the evidence lower bound (ELBO) instead. However, maximum likelihood training (whether exact or approximate) does not necessarily result in a good latent representation, as we demonstrate both theoretically and empirically. In particular, we derive variational lower and upper bounds on the mutual information between the input and the latent variable, and use these bounds to derive a rate-distortion curve that characterizes the tradeoff between compression and reconstruction accuracy. Using this framework, we demonstrate that there is a family of models with identical ELBO, but different quantitative and qualitative characteristics. Our framework also suggests a simple new method to ensure that latent variable models with powerful stochastic decoders do not ignore their latent code.

ABSTRACT We present a new approach for detecting related crime series, by unsupervised learning of the latent feature embeddings from narratives of crime record via the Gaussian-Bernoulli Restricted Boltzmann Machine (GBRBM). This is a drastically different approach from prior work on crime analysis, which typically considers only time and location and at most category information. After the embedding, related cases are closer to each other in the Euclidean feature space, and the unrelated cases are far apart, which is a good property can enable subsequent analysis such as detection and clustering of related cases. Experiments over several series of related crime incidents hand labeled by the Atlanta Police Department reveal the promise of our embedding methods. Index Terms-- Unsupervised learning, crime data analysis, feature embeddings, neural networks 1. INTRODUCTION A fundamental and one of the most challenging tasks in crime analysis is to find related crime series [1], which are committed by the same individual or group.