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.

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.

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].

We investigate an algorithm named histogram transform ensembles (HTE) density estimator whose effectiveness is supported by both solid theoretical analysis and significant experimental performance. On the theoretical side, by decomposing the error term into approximation error and estimation error, we are able to conduct the following analysis: First of all, we establish the universal consistency under $L_1(\mu)$-norm. Secondly, under the assumption that the underlying density function resides in the H\"{o}lder space $C^{0,\alpha}$, we prove almost optimal convergence rates for both single and ensemble density estimators under $L_1(\mu)$-norm and $L_{\infty}(\mu)$-norm for different tail distributions, whereas in contrast, for its subspace $C^{1,\alpha}$ consisting of smoother functions, almost optimal convergence rates can only be established for the ensembles and the lower bound of the single estimators illustrates the benefits of ensembles over single density estimators. In the experiments, we first carry out simulations to illustrate that histogram transform ensembles surpass single histogram transforms, which offers powerful evidence to support the theoretical results in the space $C^{1,\alpha}$. Moreover, to further exert the experimental performances, we propose an adaptive version of HTE and study the parameters by generating several synthetic datasets with diversities in dimensions and distributions. Last but not least, real data experiments with other state-of-the-art density estimators demonstrate the accuracy of the adaptive HTE algorithm.

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 many real-world applications of machine learning, data are distributed across many clients and cannot leave the devices they are stored on. Furthermore, each client's data, computational resources and communication constraints may be very different. This setting is known as federated learning, in which privacy is a key concern. Differential privacy is commonly used to provide mathematical privacy guarantees. This work, to the best of our knowledge, is the first to consider federated, differentially private, Bayesian learning. We build on Partitioned Variational Inference (PVI) which was recently developed to support approximate Bayesian inference in the federated setting. We modify the client-side optimisation of PVI to provide an (${\epsilon}$, ${\delta}$)-DP guarantee. We show that it is possible to learn moderately private logistic regression models in the federated setting that achieve similar performance to models trained non-privately on centralised data.

Graphical causal inference as pioneered by Judea Pearl arose from research on artificial intelligence (AI), and for a long time had little connection to the field of machine learning. This article discusses where links have been and should be established, introducing key concepts along the way. It argues that the hard open problems of machine learning and AI are intrinsically related to causality, and explains how the field is beginning to understand them.

Differential privacy is a cryptographically-motivated approach to privacy that has become a very active field of research over the last decade in theoretical computer science and machine learning. In this paradigm one assumes there is a trusted curator who holds the data of individuals in a database and the goal of privacy is to simultaneously protect individual data while allowing the release of global characteristics of the database. In this setting we introduce a general framework for parametric inference with differential privacy guarantees. We first obtain differentially private estimators based on bounded influence M-estimators by leveraging their gross-error sensitivity in the calibration of a noise term added to them in order to ensure privacy. We then show how a similar construction can also be applied to construct differentially private test statistics analogous to the Wald, score and likelihood ratio tests. We provide statistical guarantees for all our proposals via an asymptotic analysis. An interesting consequence of our results is to further clarify the connection between differential privacy and robust statistics. In particular, we demonstrate that differential privacy is a weaker stability requirement than infinitesimal robustness, and show that robust M-estimators can be easily randomized in order to guarantee both differential privacy and robustness towards the presence of contaminated data. We illustrate our results both on simulated and real data.

The data type, missing data and, anomalies can be defined in broad terms as follows: The data type is the common characteristic that is expected to be shared by entries in a column, such as integers, strings, IP addresses, dates, etc., while missing data denotes an absence of a data value which can be encoded in various ways, and anomalies refer to values whose types differ from the given column type or the missing type. In order to model above types, we have developed PFSMs that can generate values from the corresponding domains. This, in turn, allows us to calculate the probability of a given data value being generated by a particular PFSM. We then combine these PFSMs in our model such that a data column x can be annotated via probabilistic inference in the proposed model, i.e., given a column of data, we can infer column type, and rows with missing and anomalous values.

Learning models with discrete latent variables using stochastic gradient descent remains a challenge due to the high variance of gradient estimates. Modern variance reduction techniques mostly consider categorical distributions and have limited applicability when the number of possible outcomes becomes large. In this work, we consider models with latent permutations and propose control variates for the Plackett-Luce distribution. In particular, the control variates allow us to optimize black-box functions over permutations using stochastic gradient descent. To illustrate the approach, we consider a variety of causal structure learning tasks for continuous and discrete data. We show that our method outperforms competitive relaxation-based optimization methods and is also applicable to non-differentiable score functions.