Hamiltonian Monte Carlo (HMC) is a state-of-the-art Markov chain Monte Carlo sampling algorithm for drawing samples from smooth probability densities over continuous spaces. We study the variant most widely used in practice, Metropolized HMC with the St\"{o}rmer-Verlet or leapfrog integrator, and make two primary contributions. First, we provide a non-asymptotic upper bound on the mixing time of the Metropolized HMC with explicit choices of stepsize and number of leapfrog steps. This bound gives a precise quantification of the faster convergence of Metropolized HMC relative to simpler MCMC algorithms such as the Metropolized random walk, or Metropolized Langevin algorithm. Second, we provide a general framework for sharpening mixing time bounds Markov chains initialized at a substantial distance from the target distribution over continuous spaces. We apply this sharpening device to the Metropolized random walk and Langevin algorithms, thereby obtaining improved mixing time bounds from a non-warm initial distribution.

We consider the problem of selecting the best estimator among a family of Tikhonov regularized estimators, or, alternatively, to select a linear combination of these regularizers that is as good as the best regularizer in the family. Our theory reveals that if the Tikhonov regularizers share the same penalty matrix with different tuning parameters, a convex procedure based on $Q$-aggregation achieves the mean square error of the best estimator, up to a small error term no larger than $C\sigma^2$, where $\sigma^2$ is the noise level and $C>0$ is an absolute constant. Remarkably, the error term does not depend on the penalty matrix or the number of estimators as long as they share the same penalty matrix, i.e., it applies to any grid of tuning parameters, no matter how large the cardinality of the grid is. This reveals the surprising "cost-free" nature of optimally tuning Tikhonov regularizers, in striking contrast with the existing literature on aggregation of estimators where one typically has to pay a cost of $\sigma^2\log(M)$ where $M$ is the number of estimators in the family. The result holds, more generally, for any family of ordered linear smoothers. This encompasses Ridge regression as well as Principal Component Regression. The result is extended to the problem of tuning Tikhonov regularizers with different penalty matrices.

Intrinsic rewards are introduced to simulate how human intelligence works; they are usually evaluated by intrinsically-motivated play, i.e., playing games without extrinsic rewards but evaluated with extrinsic rewards. However, none of the existing intrinsic reward approaches can achieve human-level performance under this very challenging setting of intrinsically-motivated play. In this work, we propose a novel megalomania-driven intrinsic reward (called \emph{mega-reward}), which, to our knowledge, is the first approach that achieves human-level performance in intrinsically-motivated play. Intuitively, mega-reward comes from the observation that infants' intelligence develops when they try to gain more control on entities in an environment; therefore, mega-reward aims to maximize the control capabilities of agents on given entities in a given environment. To formalize mega-reward, a relational transition model is proposed to bridge the gaps between direct and latent control. Experimental studies show that mega-reward can (i) greatly outperform all state-of-the-art intrinsic reward approaches, (ii) generally achieves the same level of performance as Ex-PPO and professional human-level scores; and (iii) has also superior performance when it is incorporated with extrinsic reward.

Generative adversarial nets (GAN) has been successfully introduced for generating text to alleviate the exposure bias. However, discriminators in these models only evaluate the entire sequence, which causes feedback sparsity and mode collapse. To tackle these problems, we propose a novel mechanism. It first segments the entire sequence into several sub-sequences. Then these sub-sequences, together with the entire sequence, are evaluated individually by the discriminator. At last these feedback signals are all used to guide the learning of GAN. This mechanism learns the generation of both the entire sequence and the sub-sequences simultaneously. Learning to generate sub-sequences is easy and is helpful in generating an entire sequence. It is easy to improve the existing GAN-based models with this mechanism. We rebuild three previous well-designed models with our mechanism, and the experimental results on benchmark data show these models are improved significantly, the best one outperforms the state-of-the-art model.\footnote[1]{All code and data are available at https://github.com/liyzcj/seggan.git

While neural language models have recently demonstrated impressive performance in unconditional text generation, controllable generation and manipulation of text remain challenging. Latent variable generative models provide a natural approach for control, but their application to text has proven more difficult than to images. Models such as variational autoencoders may suffer from posterior collapse or learning an irregular latent geometry. We propose to instead employ adversarial autoencoders (AAEs) and add local perturbations by randomly replacing/removing words from input sentences during training. Within the prior enforced by the adversary, structured perturbations in the data space begin to carve and organize the latent space. Theoretically, we prove that perturbations encourage similar sentences to map to similar latent representations. Experimentally, we investigate the trade-off between text-generation and autoencoder-reconstruction capabilities. Our straightforward approach significantly improves over regular AAEs as well as other autoencoders, and enables altering the tense/sentiment of sentences through simple addition of a fixed vector offset to their latent representation.

It seems to be a pearl of conventional wisdom that parameter learning in deep sum-product networks is surprisingly fast compared to shallow mixture models. This paper examines the effects of overparameterization in sum-product networks on the speed of parameter optimisation. Using theoretical analysis and empirical experiments, we show that deep sum-product networks exhibit an implicit acceleration compared to their shallow counterpart. In fact, gradient-based optimisation in deep tree-structured sum-product networks is equal to gradient ascend with adaptive and time-varying learning rates and additional momentum terms.

In many high-dimensional estimation problems the main task consists in minimizing a cost function, which is often strongly non-convex when scanned in the space of parameters to be estimated. A standard solution to flatten the corresponding rough landscape consists in summing the losses associated to different data points and obtain a smoother empirical risk. Here we propose a complementary method that works for a single data point. The main idea is that a large amount of the roughness is uncorrelated in different parts of the landscape. One can then substantially reduce the noise by evaluating an empirical average of the gradient obtained as a sum over many random independent positions in the space of parameters to be optimized. We present an algorithm, called Replicated Gradient Descent, based on this idea and we apply it to tensor PCA, which is a very hard estimation problem. We show that Replicated Gradient Descent over-performs physical algorithms such as gradient descent and approximate message passing and matches the best algorithmic thresholds known so far, obtained by tensor unfolding and methods based on sum-of-squares.

Self-explaining models are models that reveal decision making parameters in an interpretable manner so that the model reasoning process can be directly understood by human beings. General Linear Models (GLMs) are self-explaining because the model weights directly show how each feature contributes to the output value. However, deep neural networks (DNNs) are in general not self-explaining due to the non-linearity of the activation functions, complex architectures, obscure feature extraction and transformation process. In this work, we illustrate the fact that existing deep architectures are hard to interpret because each hidden layer carries a mix of low level features and high level features. As a solution, we propose a novel feature leveling architecture that isolates low level features from high level features on a per-layer basis to better utilize the GLM layer in the proposed architecture for interpretation. Experimental results show that our modified models are able to achieve competitive results comparing to mainstream architectures on standard datasets while being more self-explainable. Our implementations and configurations are publicly available for reproductions†.

Probabilistic approach to Boolean matrix factorization can provide solutions robust against noise and missing values with linear computational complexity. However, the assumption about latent factors can be problematic in real world applications. This study proposed a new probabilistic algorithm free of assumptions of latent factors, while retaining the advantages of previous algorithms. Real data experiment showed that our algorithm was favourably compared with current state-of-the-art probabilistic algorithms.

We present a comprehensive study of multilayer neural networks with binary activation, relying on the PAC-Bayesian theory. Our contributions are twofold: (i) we develop an end-to-end framework to train a binary activated deep neural network, overcoming the fact that binary activation function is non-differentiable; (ii) we provide nonvacuous PAC-Bayesian generalization bounds for binary activated deep neural networks. Noteworthy, our results are obtained by minimizing the expected loss of an architecture-dependent aggregation of binary activated deep neural networks. The performance of our approach is assessed on a thorough numerical experiment protocol on real-life datasets.