We propose a novel online learning algorithm, called SpCoSLAM 2.0, for spatial concepts and lexical acquisition with high accuracy and scalability. Previously, we proposed SpCoSLAM as an online learning algorithm based on unsupervised Bayesian probabilistic model that integrates multimodal place categorization, lexical acquisition, and SLAM. However, our previous algorithm had limited estimation accuracy owing to the influence of the early stages of learning, and increased computational complexity with added training data. Therefore, we introduce techniques such as fixed-lag rejuvenation to reduce the calculation time while maintaining an accuracy higher than that of the previous algorithm. The results show that, in terms of estimation accuracy, the proposed algorithm exceeds the previous algorithm and is comparable to batch learning. In addition, the calculation time of the proposed algorithm does not depend on the amount of training data and becomes constant for each step of the scalable algorithm. Our approach will contribute to the realization of long-term spatial language interactions between humans and robots.

I find myself coming back to the same few pictures when explaining basic machine learning concepts. Below is a list I find most illuminating. Plots of polynomials having various orders M, shown as red curves, fitted to the data set generated by the green curve. Why Bayesian inference embodies Occam's razor. This figure gives the basic intuition for why complex models can turn out to be less probable.

State space models (SSM) have been widely applied for the analysis and visualization of large sequential datasets. Sequential Monte Carlo (SMC) is a very popular particle-based method to sample latent states from intractable posteriors. However, SSM is significantly influenced by the choice of the proposal. Recently Hamiltonian Monte Carlo (HMC) sampling has shown success in many practical problems. In this paper, we propose an SMC augmented by HMC (HSMC) for inference and model learning of nonlinear SSM, which can exempt us from learning proposals and reduce the model complexity significantly. Based on the measure preserving property of HMC, the particles directly generated by transition function can approximate the posterior of latent states arbitrarily well. In order to better adapt to the local geometry of latent space, the HMC is conducted on Riemannian manifold defined by a positive definite metric. In addition, we show that the proposed HSMC method can improve SSMs realized by both Gaussian Processes (GP) and Neural Network (NN).

This paper presents a multi-dimensional computational method to predict the spatial variation data inside and across multiple dies of a wafer. This technique is based on tensor computation. A tensor is a high-dimensional generalization of a matrix or a vector. By exploiting the hidden low-rank property of a high-dimensional data array, the large amount of unknown variation testing data may be predicted from a few random measurement samples. The tensor rank, which decides the complexity of a tensor representation, is decided by an available variational Bayesian approach. Our approach is validated by a practical chip testing data set, and it can be easily generalized to characterize the process variations of multiple wafers. Our approach is more efficient than the previous virtual probe techniques in terms of memory and computational cost when handling high-dimensional chip testing data.

To use machine learning in high stakes applications (e.g. medicine), we need tools for building confidence in the system and evaluating whether it is reliable. Methods to improve model reliability are often applied at train time (e.g. using Bayesian inference to obtain uncertainty estimates). An alternative is to audit a fixed model subsequent to training. In this paper, we describe resampling uncertainty estimation (RUE), an algorithm to audit the pointwise reliability of predictions. Intuitively, RUE estimates the amount that a single prediction would change if the model had been fit on different training data drawn from the same distribution by using the gradient and Hessian of the model's loss on training data. Experimentally, we show that RUE more effectively detects inaccurate predictions than existing tools for auditing reliability subsequent to training. We also show that RUE can create predictive distributions that are competitive with state-of-the-art methods like Monte Carlo dropout, probabilistic backpropagation, and deep ensembles, but does not depend on specific algorithms at train-time like these methods do.

Kernel Density Estimation is a very popular technique of approximating a density function from samples. The accuracy is generally well-understood and depends, roughly speaking, on the kernel decay and local smoothness of the true density. However concrete statements in the literature are often invoked in very specific settings (simplified or overly conservative assumptions) or miss important but subtle points (e.g. it is common to heuristically apply Taylor's expansion globally without referring to compactness). The contribution of this paper is twofold (a) we demonstrate that, when the bandwidth is an arbitrary invertible matrix going to zero, it is necessary to keep a certain balance between the \emph{kernel decay} and \emph{magnitudes of bandwidth eigenvalues}; in fact, without the sufficient decay the estimates may not be even bounded (b) we give a rigorous derivation of bounds with explicit constants for the bias, under possibly minimal assumptions. This connects the kernel decay, bandwidth norm, bandwidth determinant and density smoothness. It has been folklore that the issue with Taylor's formula can be fixed with more complicated assumptions on the density (for example p. 95 of "Kernel Smoothing" by Wand and Jones); we show that this is actually not necessary and can be handled by the kernel decay alone.

Low-rank matrix factorization (LRMF) has received much popularity owing to its successful applications in both computer vision and data mining. By assuming the noise term to come from a Gaussian, Laplace or a mixture of Gaussian distributions, significant efforts have been made on optimizing the (weighted) $L_1$ or $L_2$-norm loss between an observed matrix and its bilinear factorization. However, the type of noise distribution is generally unknown in real applications and inappropriate assumptions will inevitably deteriorate the behavior of LRMF. On the other hand, real data are often corrupted by skew rather than symmetric noise. To tackle this problem, this paper presents a novel LRMF model called AQ-LRMF by modeling noise with a mixture of asymmetric Laplace distributions. An efficient algorithm based on the expectation-maximization (EM) algorithm is also offered to estimate the parameters involved in AQ-LRMF. The AQ-LRMF model possesses the advantage that it can approximate noise well no matter whether the real noise is symmetric or skew. The core idea of AQ-LRMF lies in solving a weighted $L_1$ problem with weights being learned from data. The experiments conducted with synthetic and real datasets show that AQ-LRMF outperforms several state-of-the-art techniques. Furthermore, AQ-LRMF also has the superiority over the other algorithms that it can capture local structural information contained in real images.

Multi-output learning aims to simultaneously predict multiple outputs given an input. It is an important learning problem due to the pressing need for sophisticated decision making in real-world applications. Inspired by big data, the 4Vs characteristics of multi-output imposes a set of challenges to multi-output learning, in terms of the volume, velocity, variety and veracity of the outputs. Increasing number of works in the literature have been devoted to the study of multi-output learning and the development of novel approaches for addressing the challenges encountered. However, it lacks a comprehensive overview on different types of challenges of multi-output learning brought by the characteristics of the multiple outputs and the techniques proposed to overcome the challenges. This paper thus attempts to fill in this gap to provide a comprehensive review on this area. We first introduce different stages of the life cycle of the output labels. Then we present the paradigm on multi-output learning, including its myriads of output structures, definitions of its different sub-problems, model evaluation metrics and popular data repositories used in the study. Subsequently, we review a number of state-of-the-art multi-output learning methods, which are categorized based on the challenges.

Strong worst-case performance bounds for episodic reinforcement learning exist but fortunately in practice RL algorithms perform much better than such bounds would predict. Algorithms and theory that provide strong problem-dependent bounds could help illuminate the key features of what makes a RL problem hard and reduce the barrier to using RL algorithms in practice. As a step towards this we derive an algorithm for finite horizon discrete MDPs and associated analysis that both yields state-of-the art worst-case regret bounds in the dominant terms and yields substantially tighter bounds if the RL environment has small environmental norm, which is a function of the variance of the next-state value functions. An important benefit of our algorithmic is that it does not require apriori knowledge of a bound on the environmental norm. As a result of our analysis, we also help address an open learning theory question~\cite{jiang2018open} about episodic MDPs with a constant upper-bound on the sum of rewards, providing a regret bound with no $H$-dependence in the leading term that scales a polynomial function of the number of episodes.

We show tight convergence rate bounds for gradient descent and MM algorithms for maximum likelihood estimation and maximum aposteriori probability estimation of a popular Bayesian inference method for generalized Bradley-Terry models. This class of models includes the Bradley-Terry model of paired comparisons, the Rao-Kupper model of paired comparisons with ties, the Luce choice model, and the Plackett-Luce ranking model. Our results show that MM algorithms have same convergence rates as gradient descent algorithms up to constant factors. For the maximum likelihood estimation, the convergence is linear with the rate crucially determined by the algebraic connectivity of the matrix of item pair co-occurrences in observed comparison data. For the Bayesian inference, the convergence rate is also linear, with the rate determined by a parameter of the prior distribution in a way that can make convergence arbitrarily slow for small values of this parameter. We propose a simple, first-order acceleration method that resolves the slow convergence issue.