The uncertainty estimation is critical in real-world decision making applications, especially when distributional shift between the training and test data are prevalent. Many calibration methods in the literature have been proposed to improve the predictive uncertainty of DNNs which are generally not well-calibrated. However, none of them is specifically designed to work properly under domain shift condition. In this paper, we propose Unsupervised Temperature Scaling (UTS) as a robust calibration method to domain shift. It exploits unlabeled test samples instead of the training one to adjust the uncertainty prediction of deep models towards the test distribution. UTS utilizes a novel loss function, weighted NLL, which allows unsupervised calibration. We evaluate UTS on a wide range of model-datasets to show the possibility of calibration without labels and demonstrate the robustness of UTS compared to other methods (e.g., TS, MCdropout, SVI, ensembles) in shifted domains. The predictive distributions provided by Deep Neural Networks (DNNs) have been increasingly used for decision-support systems, for applications ranging from medical diagnoses assistance (Esteva et al., 2017) to self-driving cars (Bojarski et al., 2016). In DNNs, the predictive distributions usually corresponds to the output of a softmax layer, which is typically interpreted as the confidence over the different classes. The i.i.d hypothesis made in learning usually assumes that the data distributions over the classes are the same at learning and inference time. However, in real-world applications, the distribution of data at inference time (i.e., the test data) may shift and actually be different from the original training distribution - corresponding to distribution shift in representation of data which we refer that as domain shift. For instance, in image classification problem, domain shift happens when the test images are different in illumination, view point, resolution, background or intensity noise from the training set. However, they are the same classification problem with the same objects occurance rate.

--This research proposes a new (old) metric for evaluating goodness of fit in topic models, the coefficient of determination, or R 2 . Within the context of topic modeling, R 2 has the same interpretation that it does when used in a broader class of statistical models. Reporting R 2 with topic models addresses two current problems in topic modeling: a lack of standard cross-contextual evaluation metrics for topic modeling and ease of communication with lay audiences. The author proposes that R 2 should be reported as a standard metric when constructing topic models. I NTRODUCTION According to an often-quoted but never cited definition, "the goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question." 1 Goodness of fit measures vary with the goals of those constructing the statistical model. Inferential goals may emphasize in-sample fit while predictive goals may emphasize out-of-sample fit. Prior information may be included in the goodness of fit measure for Bayesian models, or it may not. Goodness of fit measures may include methods to correct for model overfitting. In short, goodness of fit measures the performance of a statistical model against the ground truth of observed data. Fitting the data well is generally a necessary--though not sufficient--condition for trust in a statistical model, whatever its goals. Of course, goodness of fit is only one concern in statistical modeling.

Recently, there has been growing interest in estimating optimal treatment regimes which are individualized decision rules that can achieve maximal average outcomes. This paper considers the problem of inference for optimal treatment regimes in the model-free setting, where the specification of an outcome regression model is not needed. Existing model-free estimators are usually not suitable for the purpose of inference because they either have nonstandard asymptotic distributions, or are designed to achieve fisher-consistent classification performance. This paper first studies a smoothed robust estimator that directly targets estimating the parameters corresponding to the Bayes decision rule for estimating the optimal treatment regime. This estimator is shown to have an asymptotic normal distribution. Furthermore, it is proved that a resampling procedure provides asymptotically accurate inference for both the parameters indexing the optimal treatment regime and the optimal value function. A new algorithm is developed to calculate the proposed estimator with substantially improved speed and stability. Numerical results demonstrate the satisfactory performance of the new methods.

Random projections offer an appealing and flexible approach to a wide range of large-scale statistical problems. They are particularly useful in high-dimensional settings, where we have many covariates recorded for each observation. In classification problems there are two general techniques using random projections. The first involves many projections in an ensemble -- the idea here is to aggregate the results after applying different random projections, with the aim of achieving superior statistical accuracy. The second class of methods include hashing and sketching techniques, which are straightforward ways to reduce the complexity of a problem, perhaps therefore with a huge computational saving, while approximately preserving the statistical efficiency.

Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of independent identical Gaussian noise. Probabilistic PCA (PPCA) and its variants have been extensively studied for decades. Most of them assume the underlying noise follows a certain independent identical distribution. However, the noise in the real world is usually complicated and structured. To address this challenge, some non-linear variants of PPCA have been proposed. But those methods are generally difficult to interpret. To this end, we propose a powerful and intuitive PCA method (MN-PCA) through modeling the graphical noise by the matrix normal distribution, which enables us to explore the structure of noise in both the feature space and the sample space. MN-PCA obtains a low-rank representation of data and the structure of noise simultaneously. And it can be explained as approximating data over the generalized Mahalanobis distance. We develop two algorithms to solve this model: one maximizes the regularized likelihood, the other exploits the Wasserstein distance, which is more robust. Extensive experiments on various data demonstrate their effectiveness.

Recent years have witnessed significant advances in reinforcement learning (RL), which has registered great success in solving various sequential decision-making problems in machine learning. Most of the successful RL applications, e.g., the games of Go and Poker, robotics, and autonomous driving, involve the participation of more than one single agent, which naturally fall into the realm of multi-agent RL (MARL), a domain with a relatively long history, and has recently re-emerged due to advances in single-agent RL techniques. Though empirically successful, theoretical foundations for MARL are relatively lacking in the literature. In this chapter, we provide a selective overview of MARL, with focus on algorithms backed by theoretical analysis. More specifically, we review the theoretical results of MARL algorithms mainly within two representative frameworks, Markov/stochastic games and extensive-form games, in accordance with the types of tasks they address, i.e., fully cooperative, fully competitive, and a mix of the two. We also introduce several significant but challenging applications of these algorithms. Orthogonal to the existing reviews on MARL, we highlight several new angles and taxonomies of MARL theory, including learning in extensive-form games, decentralized MARL with networked agents, MARL in the mean-field regime, (non-)convergence of policy-based methods for learning in games, etc. Some of the new angles extrapolate from our own research endeavors and interests. Our overall goal with this chapter is, beyond providing an assessment of the current state of the field on the mark, to identify fruitful future research directions on theoretical studies of MARL. We expect this chapter to serve as continuing stimulus for researchers interested in working on this exciting while challenging topic.

Phase Modulation on the Hypersphere (PMH) is a power efficient modulation scheme for the load-modulated multiple-input multiple-output (MIMO) transmitters with central power amplifiers (CP A). However, it is difficult to obtain the precise channel state information (CSI), and the traditional optimal maximum likelihood (ML) detection scheme incurs high complexity which increases exponentially with the number of antennas and the number of bits carried per antenna in the PMH modulation. To detect the PMH signals without knowing the prior CSI, we first propose a signal detection scheme, termed as the hypersphere clustering scheme based on the expectation maximization (EM) algorithm with maximum likelihood detection (HEM-ML). By leveraging machine learning, the proposed detection scheme can accurately obtain information of the channel from a few of the received symbols with little resource cost and achieve comparable detection results as that of the optimal ML detector. To further reduce the computational complexity in the ML detection in HEM-ML, we also propose the second signal detection scheme, termed as the hypersphere clustering scheme based on the EM algorithm with KD-tree detection (HEM-KD). The CSI obtained from the EM algorithm is used to build a spatial KD-tree receiver codebook and the signal detection problem can be transformed into a nearest neighbor search (NNS) problem. The detection complexity of HEM-KD is significantly reduced without any detection performance loss as compared to HEM-ML. Extensive simulation results verify the effectiveness of our proposed detection schemes. I NTRODUCTION The fifth generation (5G) wireless communication network is forecasted to provide over 1000 times higher capacity than the current system. In addition to dramatically expanding the available bandwidth, multiple-input multiple-output (MIMO) technology is playing a key role in improving the spectral efficiency (SE) and enhancing the throughput in the future wireless cellular communication systems [1]. This ambitious goal will however cause an inevitable energy consumption problem, thus limiting the number of the antennas at the base station (BS) and the user terminals in practice [2]. In the traditional design of the MIMO transceivers, each antenna is connected with one distinct radio frequency (RF) chain which includes a power amplifier (P A). This kind of structure enables the power consumption of the transmission to grow linearly with the number of the antennas. In addition, the use of Orthogonal Frequency Division Multiplexing (OFDM) signals in massive MIMO systems leads to a high peak-to-average power ratios (P APR) and exacerbates the costs of P As, thus reducing the power efficiency. On the other hand, to alleviate the effects of mutual coupling and correlated fading, the antennas should be set at least half of a wavelength apart from each other, which will inevitably cause the size problem [3].

Mutual information is widely applied to learn latent representations of observations, whilst its implication in classification neural networks remain to be better explained. In this paper, we show that optimising the parameters of classification neural networks with softmax cross-entropy is equivalent to maximising the mutual information between inputs and labels under the balanced data assumption. Through the experiments on synthetic and real datasets, we show that softmax cross-entropy can estimate mutual information approximately. When applied to image classification, this relation helps approximate the point-wise mutual information between an input image and a label without modifying the network structure. In this end, we propose infoCAM, informative class activation map, which highlights regions of the input image that are the most relevant to a given label based on differences in information. The activation map helps localise the target object in an image. Through the experiments on the semi-supervised object localisation task with two real-world datasets, we evaluate the effectiveness of the information-theoretic approach.

In reinforcement learning (RL), agents often operate in partially observed and uncertain environments. Model-based RL suggests that this is best achieved by learning and exploiting a probabilistic model of the world. 'Active inference' is an emerging normative framework in cognitive and computational neuroscience that offers a unifying account of how biological agents achieve this. On this framework, inference, learning and action emerge from a single imperative to maximize the Bayesian evidence for a niched model of the world. However, implementations of this process have thus far been restricted to low-dimensional and idealized situations. Here, we present a working implementation of active inference that applies to high-dimensional tasks, with proof-of-principle results demonstrating efficient exploration and an order of magnitude increase in sample efficiency over strong model-free baselines. Our results demonstrate the feasibility of applying active inference at scale and highlight the operational homologies between active inference and current model-based approaches to RL.

In response to the continuing research interest in computational semantic analysis, we have proposed a new task for SemEval-2010: multi-way classification of mutually exclusive semantic relations between pairs of nominals. The task is designed to compare different approaches to the problem and to provide a standard testbed for future research. In this paper, we define the task, describe the creation of the datasets, and discuss the results of the participating 28 systems submitted by 10 teams.