We propose novel dynamic multiscale graph neural networks (DMGNN) to predict 3D skeleton-based human motions. The core idea of DMGNN is to use a multiscale graph to comprehensively model the internal relations of a human body for motion feature learning. This multiscale graph is adaptive during training and dynamic across network layers. Based on this graph, we propose a multiscale graph computational unit (MGCU) to extract features at individual scales and fuse features across scales. The entire model is action-category-agnostic and follows an encoder-decoder framework. The encoder consists of a sequence of MGCUs to learn motion features. The decoder uses a proposed graph-based gate recurrent unit to generate future poses. Extensive experiments show that the proposed DMGNN outperforms state-of-the-art methods in both short and long-term predictions on the datasets of Human 3.6M and CMU Mocap. We further investigate the learned multiscale graphs for the interpretability. The codes could be downloaded from https://github.com/limaosen0/DMGNN.

We address the problem of policy evaluation in discounted Markov decision processes, and provide instance-dependent guarantees on the $\ell_\infty$-error under a generative model. We establish both asymptotic and non-asymptotic versions of local minimax lower bounds for policy evaluation, thereby providing an instance-dependent baseline by which to compare algorithms. Theory-inspired simulations show that the widely-used temporal difference (TD) algorithm is strictly suboptimal when evaluated in a non-asymptotic setting, even when combined with Polyak-Ruppert iterate averaging. We remedy this issue by introducing and analyzing variance-reduced forms of stochastic approximation, showing that they achieve non-asymptotic, instance-dependent optimality up to logarithmic factors.

In this paper, we solve the problem of predicting the next locations of the moving objects with a historical dataset of trajectories. We present a Next Location Predictor with Markov Modeling (NLPMM) which has the following advantages: (1) it considers both individual and collective movement patterns in making prediction, (2) it is effective even when the trajectory data is sparse, (3) it considers the time factor and builds models that are suited to different time periods. We have conducted extensive experiments in a real dataset, and the results demonstrate the superiority of NLPMM over existing methods.

Predicting and modeling human behavior and finding trends within human decision-making process is a major social sciences'problem. Rock Paper Scissors (RPS) is the fundamental strategic question in many game theory problems and real-world competitions. Finding the right approach to beat a particular human opponent is challenging. Here we use Markov Chains with set chain lengths as the single AIs (artificial intelligences) to compete against humans in iterated RPS game. This is the first time that an AI algorithm is applied in RPS human competition behavior studies. We developed an architecture of multi-AI with changeable parameters to adapt to different competition strategies. We introduce a parameter "focus length" (an integer of e.g. 5 or 10) to control the speed and sensitivity for our multi-AI to adapt to the opponent's strategy change. We experimented with 52 different people, each playing 300 rounds continuously against one specific multi-AI model, and demonstrated that our strategy could win over more than 95% of human opponents.

In high-dimensional data space, semi-supervised feature learning based on Euclidean distance shows instability under a broad set of conditions. Furthermore, the scarcity and high cost of labels prompt us to explore new semi-supervised learning methods with the fewest labels. In this paper, we develop a novel Minor Constraint Disturbances-based Deep Semi-supervised Feature Learning framework (MCD-DSFL) from the perspective of probability distribution for feature representation. There are two fundamental modules in the proposed framework: one is a Minor Constraint Disturbances-based restricted Boltzmann machine with Gaussian visible units (MCDGRBM) for modelling continuous data and the other is a Minor Constraint Disturbances-based restricted Boltzmann machine (MCDRBM) for modelling binary data. The Minor Constraint Disturbances (MCD) consist of less instance-level constraints which are produced by only two randomly selected labels from each class. The Kullback-Leibler (KL) divergences of the MCD are fused into the Contrastive Divergence (CD) learning for training the proposed MCDGRBM and MCDRBM models. Then, the probability distributions of hidden layer features are as similar as possible in the same class and they are as dissimilar as possible in the different classes simultaneously. Despite the weak influence of the MCD for our shallow models (MCDGRBM and MCDRBM), the proposed deep MCD-DSFL framework improves the representation capability significantly under its leverage effect. The semi-supervised strategy based on the KL divergence of the MCD significantly reduces the reliance on the labels and improves the stability of the semi-supervised feature learning in high-dimensional space simultaneously.

Smart home environments equipped with distributed sensor networks are capable of helping people by providing services related to health, emergency detection or daily routine management. A backbone to these systems relies often on the system's ability to track and detect activities performed by the users in their home. Despite the continuous progress in the area of activity recognition in smart homes, many systems make a strong underlying assumption that the number of occupants in the home at any given moment of time is always known. Estimating the number of persons in a Smart Home at each time step remains a challenge nowadays. Indeed, unlike most (crowd) counting solution which are based on computer vision techniques, the sensors considered in a Smart Home are often very simple and do not offer individually a good overview of the situation. The data gathered needs therefore to be fused in order to infer useful information. This paper aims at addressing this challenge and presents a probabilistic approach able to estimate the number of persons in the environment at each time step. This approach works in two steps: first, an estimate of the number of persons present in the environment is done using a Constraint Satisfaction Problem solver, based on the topology of the sensor network and the sensor activation pattern at this time point. Then, a Hidden Markov Model refines this estimate by considering the uncertainty related to the sensors. Using both simulated and real data, our method has been tested and validated on two smart homes of different sizes and configuration and demonstrates the ability to accurately estimate the number of inhabitants.

One of the core challenges in the field of control theory and reinforcement learning is adaptive control. It is the problem of controlling dynamical systems when the dynamics of the systems are unknown to the decision-making agents. In adaptive control, agents interact with given systems in order to explore and control them while the long-term objective is to minimize the overall average associated costs. The agent has to balance between exploration and exploitation, learn the dynamics, strategize for further exploration, and exploit the estimation to minimize the overall costs. The sequential nature of agent-system interaction results in challenges in the system identifying, estimation, and control under uncertainty, and these challenges are magnified when the systems are partially observable, i.e. contain hidden underlying dynamics. In the linear systems, when the underlying dynamics are fully observable, the asymptotic optimality of estimation methods has been the topic of study in the last decades [Lai et al., 1982, Lai and Wei, 1987]. Recently, novel techniques and learning algorithms have been developed to study the finite-time behavior of adaptive control algorithms and shed light on the design of optimal methods [Peña et al., 2009, Fiechter, 1997, Abbasi-Yadkori and Szepesvári, 2011]. In particular, Abbasi-Yadkori and Szepesvári [2011] proposes to use the principle of optimism in the face of uncertainty (OFU) to balance exploration and exploitation in LQR, where the state of the system is observable.

The best way to calculate statistics from medical data is to use the data of individual patients. In some settings, this data is difficult to obtain due to privacy restrictions. In Germany, for example, it is not possible to pool routine data from different hospitals for research purposes without the consent of the patients. The DataSHIELD software provides an infrastructure and a set of statistical methods for joint analyses of distributed data. The contained algorithms are reformulated to work with aggregated data from the participating sites instead of the individual data. If a desired algorithm is not implemented in DataSHIELD or cannot be reformulated in such a way, using artificial data is an alternative. We present a methodology together with a software implementation that builds on DataSHIELD to create artificial data that preserve complex patterns from distributed individual patient data. Such data sets of artificial patients, which are not linked to real patients, can then be used for joint analyses. We use deep Boltzmann machines (DBMs) as generative models for capturing the distribution of data. For the implementation, we employ the package "BoltzmannMachines" from the Julia programming language and wrap it for use with DataSHIELD, which is based on R. As an exemplary application, we conduct a distributed analysis with DBMs on a synthetic data set, which simulates genetic variant data. Patterns from the original data can be recovered in the artificial data using hierarchical clustering of the virtual patients, demonstrating the feasibility of the approach. Our implementation adds to DataSHIELD the ability to generate artificial data that can be used for various analyses, e. g. for pattern recognition with deep learning. This also demonstrates more generally how DataSHIELD can be flexibly extended with advanced algorithms from languages other than R.

In the optimization of dynamic systems, the variables typically have constraints. Such problems can be modeled as a constrained Markov Decision Process (MDP). This paper considers a model-free approach to the problem, where the transition probabilities are not known. In the presence of peak constraints, the agent has to choose the policy to maximize the long-term average reward as well as satisfy the constraints at each time. We propose modifications to the standard Q-learning problem for unconstrained optimization to come up with an algorithm with peak constraints. The proposed algorithm is shown to achieve $O(T^{1/2+\gamma})$ regret bound for the obtained reward, and $O(T^{1-\gamma})$ regret bound for the constraint violation for any $\gamma \in(0,1/2)$ and time-horizon $T$. We note that these are the first results on regret analysis for constrained MDP, where the transition problems are not known apriori. We demonstrate the proposed algorithm on an energy harvesting problem where it outperforms state-of-the-art and performs close to the theoretical upper bound of the studied optimization problem.

Gaussian Processes (GPs) provide a powerful probabilistic framework for interpolation, forecasting, and smoothing, but have been hampered by computational scaling issues. Here we prove that for data sampled on one dimension (e.g., a time series sampled at arbitrarily-spaced intervals), approximate GP inference at any desired level of accuracy requires computational effort that scales linearly with the number of observations; this new theorem enables inference on much larger datasets than was previously feasible. To achieve this improved scaling we propose a new family of stationary covariance kernels: the Latent Exponentially Generated (LEG) family, which admits a convenient stable state-space representation that allows linear-time inference. We prove that any continuous integrable stationary kernel can be approximated arbitrarily well by some member of the LEG family. The proof draws connections to Spectral Mixture Kernels, providing new insight about the flexibility of this popular family of kernels. We propose parallelized algorithms for performing inference and learning in the LEG model, test the algorithm on real and synthetic data, and demonstrate scaling to datasets with billions of samples.