In this paper, we investigate the popular deep learning optimization routine, Adam, from the perspective of statistical moments. While Adam is an adaptive lower-order moment based (of the stochastic gradient) method, we propose an extension namely, HAdam, which uses higher order moments of the stochastic gradient. Our analysis and experiments reveal that certain higher-order moments of the stochastic gradient are able to achieve better performance compared to the vanilla Adam algorithm. We also provide some analysis of HAdam related to odd and even moments to explain some intriguing and seemingly non-intuitive empirical results.

Outlier detection is a technique in data mining that aims to detect unusual or unexpected records in the dataset. Existing outlier detection algorithms have different pros and cons and exhibit different sensitivity to noisy data such as extreme values. In this paper, we propose a novel cluster-based outlier detection algorithm named MSD-Kmeans that combines the statistical method of Mean and Standard Deviation (MSD) and the machine learning clustering algorithm K-means to detect outliers more accurately with the better control of extreme values. There are two phases in this combination method of MSD-Kmeans: (1) applying MSD algorithm to eliminate as many noisy data to minimize the interference on clusters, and (2) applying K-means algorithm to obtain local optimal clusters. We evaluate our algorithm and demonstrate its effectiveness in the context of detecting possible overcharging of taxi fares, as greedy dishonest drivers may attempt to charge high fares by detouring. We compare the performance indicators of MSD-Kmeans with those of other outlier detection algorithms, such as MSD, K-means, Z-score, MIQR and LOF, and prove that the proposed MSD-Kmeans algorithm achieves the highest measure of precision, accuracy, and F-measure. We conclude that MSD-Kmeans can be used for effective and efficient outlier detection on data of varying quality on IoT devices.

--Existing algorithms aiming to learn a binary classifier from positive (P) and unlabeled (U) data require estimating the class prior or label noise ahead of building a classification model. However, the estimation and classifier learning are normally conducted in a pipeline instead of being jointly optimized. In this paper, we propose to alternatively train the two steps using reinforcement learning. Our proposal adopts a policy network to adaptively make assumptions on the labels of unlabeled data, while a classifier is built upon the output of the policy network and provides rewards to learn a better policy. The dynamic and interactive training between the policy maker and the classifier can exploit the unlabeled data in a more effective manner and yield a significant improvement in terms of classification performance. Furthermore, we present two different approaches to represent the actions taken by the policy. The first approach considers continuous actions as soft labels, while the other uses discrete actions as hard assignment of labels for unlabeled examples. We validate the effectiveness of the proposed method on two public benchmark datasets as well as one e-commerce dataset. The results show that the proposed method is able to consistently outperform state-of-the-art methods in various settings. PU learning refers to the problem of learning from a dataset where only a subset of examples are positively labeled and the rest are not annotated at all. It is a critical task due to its prevalence in various real-world applications [1], [2], [3]. In many common situations only positive data are available, for instance, an e-commerce website may only record users who have clicked on advertisements or purchased items. Meanwhile, it is not possible to simply assume that unlabeled instances are negative.

The main goal of this work is equipping convex and nonconvex problems with Barzilai-Borwein (BB) step size. With the adaptivity of BB step sizes granted, they can fail when the objective function is not strongly convex. To overcome this challenge, the key idea here is to bridge (non)convex problems and strongly convex ones via regularization. The proposed regularization schemes are \textit{simple} yet effective. Wedding the BB step size with a variance reduction method, known as SARAH, offers a free lunch compared with vanilla SARAH in convex problems. The convergence of BB step sizes in nonconvex problems is also established and its complexity is no worse than other adaptive step sizes such as AdaGrad. As a byproduct, our regularized SARAH methods for convex functions ensure that the complexity to find $\mathbb{E}[\| \nabla f(\mathbf{x}) \|^2]\leq \epsilon$ is ${\cal O}\big( (n+\frac{1}{\sqrt{\epsilon}})\ln{\frac{1}{\epsilon}}\big)$, improving $\epsilon$ dependence over existing results. Numerical tests further validate the merits of proposed approaches.

Despite great popularity of applying softmax to map the non-normalised outputs of a neural network to a probability distribution over predicting classes, this normalised exponential transformation still seems to be artificial. A theoretic framework that incorporates softmax as an intrinsic component is still lacking. In this paper, we view neural networks embedding softmax from an information-theoretic perspective. Under this view, we can naturally and mathematically derive log-softmax as an inherent component in a neural network for evaluating the conditional mutual information between network output vectors and labels given an input datum. We show that training deterministic neural networks through maximising log-softmax is equivalent to enlarging the conditional mutual information, i.e., feeding label information into network outputs. We also generalise our informative-theoretic perspective to neural networks with stochasticity and derive information upper and lower bounds of log-softmax. In theory, such an information-theoretic view offers rationality support for embedding softmax in neural networks; in practice, we eventually demonstrate a computer vision application example of how to employ our information-theoretic view to filter out targeted objects on images.

In this article, we focus on the utilisation of reactive trajectory imitation controllers for goal-directed mobile robot navigation. We propose a topological navigation graph (TNG) - an imitation-learning-based framework for navigating through environments with intersecting trajectories. The TNG framework represents the environment as a directed graph composed of deep neural networks. Each vertex of the graph corresponds to a trajectory and is represented by a trajectory identification classifier and a trajectory imitation controller. For trajectory following, we propose the novel use of neural object detection architectures. The edges of TNG correspond to intersections between trajectories and are all represented by a classifier. We provide empirical evaluation of the proposed navigation framework and its components in simulated and real-world environments, demonstrating that TNG allows us to utilise non-goal-directed, imitation-learning methods for goal-directed autonomous navigation.

A pivotal point to be noted is that we are not dealing with a usually labeled dataset. Data for survival analysis is different from standard regression or classification problem. In survival analysis, we are dealing with censored data. Censoring is a form of missing data problem. Whenever we deal with survival analysis, we will get the training data within a study period.

Last week's post just happened to use MCMCglmm as an example of an R package that can get confused by tibble-style data frames. To make that example, I simulated some pedigree and trait data. Just for fun, let's look at the simulation code, and use MCMCglmm and AnimalINLA to get heritability estimates. Now that we have some data, we can fit a quantitative genetic pedigree model ("animal model") to estimate genetic parameters. We're going to try two methods to fit it: Markov Chain Monte Carlo and (the unfortunately named) Integrated Nested Laplace Approximation.

Abstract--Large-scale and multidimensional spatiotemporal data sets are becoming ubiquitous in many real-world applications such as monitoring urban traffic and air quality . Making predictions on these time series has become a critical challenge due to not only the large-scale and high-dimensional nature but also the considerable amount of missing data. In this paper, we propose a Bayesian temporal factorization (BTF) framework for modeling multidimensional time series--in particular spatiotemporal data--in the presence of missing values. By integrating low-rank matrix/tensor factorization and vector autoregressive (VAR) process into a single probabilistic graphical model, this framework can characterize both global and local consistencies in large-scale time series data. The graphical model allows us to effectively perform probabilistic predictions and produce uncertainty estimates without imputing those missing values. We develop efficient Gibbs sampling algorithms for model inference and test the proposed BTF framework on several real-world spatiotemporal data sets for both missing data imputation and short-term/long-term rolling prediction tasks. The numerical experiments demonstrate the superiority of the proposed BTF approaches over many state-of-the-art techniques. With recent advances in sensing technologies, large-scale and multidimensional time series data--in particular spatiotemporal data--are collected on a continuous basis from various types of sensors and applications. Making predictions on these time series, such as forecasting urban traffic states and regional air quality, serves as a foundation to many real-world applications and benefits many scientific fields [1], [2]. For example, predicting the demand and states (e.g., speed, flow) of urban traffic is essential to a wide range of intelligent transportation systems (ITS) applications, such trip planning, travel time estimation, route planning, traffic signal control, to name but a few [3]. However, given the complex spatiotemporal dependencies in these data sets, making efficient and reliable predictions for real-time applications has been a longstanding and fundamental research challenge. Despite the vast body of literature on time series analysis from many scientific areas, three emerging issues in modern sensing technologies are constantly challenging the classical modeling frameworks. First, modern time series data are often large-scale, collected from a large number of subjects/locations/sensors simultaneously .

We introduce the Mutual Information Machine (MIM), an autoencoder model for learning joint distributions over observations and latent states. The model formulation reflects two key design principles: 1) symmetry, to encourage the encoder and decoder to learn consistent factorizations of the same underlying distribution; and 2) mutual information, to encourage the learning of useful representations for downstream tasks. The objective comprises the Jensen-Shannon divergence between the encoding and decoding joint distributions, plus a mutual information term. We show that this objective can be bounded by a tractable cross-entropy loss between the true model and a parameterized approximation, and relate this to maximum likelihood estimation and variational autoencoders. Experiments show that MIM is capable of learning a latent representation with high mutual information, and good unsupervised clustering, while providing data log likelihood comparable to VAE (with a sufficiently expressive architecture).