Motivation: Ab initio protein docking represents a major challenge for optimizing a noisy and costly "black box"-like function in a high-dimensional space. Despite progress in this field, there is no docking method available for rigorous uncertainty quantification (UQ) of its solution quality (e.g. interface RMSD or iRMSD). Results: We introduce a novel algorithm, Bayesian Active Learning (BAL), for optimization and UQ of such black-box functions and flexible protein docking. BAL directly models the posterior distribution of the global optimum (or native structures for protein docking) with active sampling and posterior estimation iteratively feeding each other. Furthermore, we use complex normal modes to represent a homogeneous Euclidean conformation space suitable for high-dimension optimization and construct funnel-like energy models for encounter complexes. Over a protein docking benchmark set and a CAPRI set including homology docking, we establish that BAL significantly improve against both starting points by rigid docking and refinements by particle swarm optimization, providing for one third targets a top-3 near-native prediction. BAL also generates tight confidence intervals with half range around 25% of iRMSD and confidence level at 85%. Its estimated probability of a prediction being native or not achieves binary classification AUROC at 0.93 and AUPRC over 0.60 (compared to 0.14 by chance); and also found to help ranking predictions. To the best of our knowledge, this study represents the first uncertainty quantification solution for protein docking, with theoretical rigor and comprehensive assessment. Source codes are available at https://github.com/Shen-Lab/BAL.

Gaussian conditional random fields (GCRF) are a well-known used structured model for continuous outputs that uses multiple unstructured predictors to form its features and at the same time exploits dependence structure among outputs, which is provided by a similarity measure. In this paper, a Gaussian conditional random fields model for structured binary classification (GCRFBC) is proposed. The model is applicable to classification problems with undirected graphs, intractable for standard classification CRFs. The model representation of GCRFBC is extended by latent variables which yield some appealing properties. Thanks to the GCRF latent structure, the model becomes tractable, efficient and open to improvements previously applied to GCRF regression models. In addition, the model allows for reduction of noise, that might appear if structures were defined directly between discrete outputs. Additionally, two different forms of the algorithm are presented: GCRFBCb (GCRGBC - Bayesian) and GCRFBCnb (GCRFBC - non Bayesian). The extended method of local variational approximation of sigmoid function is used for solving empirical Bayes in Bayesian GCRFBCb variant, whereas MAP value of latent variables is the basis for learning and inference in the GCRFBCnb variant. The inference in GCRFBCb is solved by Newton-Cotes formulas for one-dimensional integration. Both models are evaluated on synthetic data and real-world data. It was shown that both models achieve better prediction performance than unstructured predictors. Furthermore, computational and memory complexity is evaluated. Advantages and disadvantages of the proposed GCRFBCb and GCRFBCnb are discussed in detail.

Is it possible to predict the motivation of players just by observing their gameplay data? Even if so, how should we measure motivation in the first place? To address the above questions, on the one end, we collect a large dataset of gameplay data from players of the popular game Tom Clancy's The Division (Ubisoft, 2016). On the other end we ask them to report their levels of competence, autonomy, relatedness and presence using the in-house designed Ubisoft Perceived Experience Questionnaire. After processing the survey responses in an ordinal fashion we employ preference learning methods, based on support vector machines, to infer the mapping between gameplay and the four motivation factors. Our key findings suggest that gameplay features are strong predictors of player motivation as the obtained models reach accuracies of near certainty, in particular, from 93% up to 97% on unseen players.

In this paper, we introduce a novel concept for learning of the parameters in a neural network. Our idea is grounded on modeling a learning problem that addresses a trade-off between (i) satisfying local objectives at each node and (ii) achieving desired data propagation through the network under (iii) local propagation constraints. We consider two types of nonlinear transforms which describe the network representations. One of the nonlinear transforms serves as activation function. The other one enables a locally adjusted, deviation corrective components to be included in the update of the network weights in order to enable attaining target specific representations at the last network node. Our learning principle not only provides insight into the understanding and the interpretation of the learning dynamics, but it offers theoretical guarantees over decoupled and parallel parameter estimation strategy that enables learning in synchronous and asynchronous mode. Numerical experiments validate the potential of our approach on image recognition task. The preliminary results show advantages in comparison to the state-of-the-art methods, w.r.t. the learning time and the network size while having competitive recognition accuracy.

Stochastic Variance-Reduced Cubic regularization (SVRC) algorithms have received increasing attention due to its improved gradient/Hessian complexities (i.e., number of queries to stochastic gradient/Hessian oracles) to find local minima for nonconvex finite-sum optimization. However, it is unclear whether existing SVRC algorithms can be further improved. Moreover, the semi-stochastic Hessian estimator adopted in existing SVRC algorithms prevents the use of Hessian-vector product-based fast cubic subproblem solvers, which makes SVRC algorithms computationally intractable for high-dimensional problems. In this paper, we first present a Stochastic Recursive Variance-Reduced Cubic regularization method (SRVRC) using a recursively updated semi-stochastic gradient and Hessian estimators. It enjoys improved gradient and Hessian complexities to find an $(\epsilon, \sqrt{\epsilon})$-approximate local minimum, and outperforms the state-of-the-art SVRC algorithms. Built upon SRVRC, we further propose a Hessian-free SRVRC algorithm, namely SRVRC$_{\text{free}}$, which only requires stochastic gradient and Hessian-vector product computations, and achieves $\tilde O(dn\epsilon^{-2} \land d\epsilon^{-3})$ runtime complexity, where $n$ is the number of component functions in the finite-sum structure, $d$ is the problem dimension, and $\epsilon$ is the optimization precision. This outperforms the best-known runtime complexity $\tilde O(d\epsilon^{-3.5})$ achieved by stochastic cubic regularization algorithm proposed in Tripuraneni et al. 2018.

Recently there has been an increasing interest in the multivariate Gaussian process (MGP) which extends the Gaussian process (GP) to deal with multiple outputs. One approach to construct the MGP and account for non-trivial commonalities amongst outputs employs a convolution process (CP). The CP is based on the idea of sharing latent functions across several convolutions. Despite the elegance of the CP construction, it provides new challenges that need yet to be tackled. First, even with a moderate number of outputs, model building is extremely prohibitive due to the huge increase in computational demands and number of parameters to be estimated. Second, the negative transfer of knowledge may occur when some outputs do not share commonalities. In this paper we address these issues. We propose a regularized pairwise modeling approach for the MGP established using CP. The key feature of our approach is to distribute the estimation of the full multivariate model into a group of bivariate GPs which are individually built. Interestingly pairwise modeling turns out to possess unique characteristics, which allows us to tackle the challenge of negative transfer through penalizing the latent function that facilitates information sharing in each bivariate model. Predictions are then made through combining predictions from the bivariate models within a Bayesian framework. The proposed method has excellent scalability when the number of outputs is large and minimizes the negative transfer of knowledge between uncorrelated outputs. Statistical guarantees for the proposed method are studied and its advantageous features are demonstrated through numerical studies.

Black-box optimizers that explore in parameter space have often been shown to outperform more sophisticated action space exploration methods developed specifically for the reinforcement learning problem. We examine these black-box methods closely to identify situations in which they are worse than action space exploration methods and those in which they are superior. Through simple theoretical analyses, we prove that complexity of exploration in parameter space depends on the dimensionality of parameter space, while complexity of exploration in action space depends on both the dimensionality of action space and horizon length. This is also demonstrated empirically by comparing simple exploration methods on several model problems, including Contextual Bandit, Linear Regression and Reinforcement Learning in continuous control.

We use self-report and electrodermal activity (EDA) wearable sensor data from 77 nights of sleep on six participants to test the efficacy of EDA data for sleep monitoring. We used factor analysis to find latent factors in the EDA data, and causal model search to find the most probable graphical model accounting for self-reported sleep efficiency (SE), sleep quality (SQ), and the latent EDA factors. Structural equation modeling was used to confirm fit of the extracted graph. Based on the generated graph, logistic regression and naive Bayes models were used to test the efficacy of the EDA data in predicting SE and SQ. Six EDA features extracted from the total signal over a night's sleep could be explained by two latent factors, EDA Magnitude and EDA Storms. EDA Magnitude performed as a strong predictor for SE to aid detection of substantial changes in time asleep. The performance of EDA Magnitured and SE in classifying SQ showed promise for wearable sleep monitoring applications. However, our data suggest that obtaining a more accurate sensor-based measure of SE will be necessary before smaller changes in SQ can be detected from EDA sensor data alone.

We introduce a novel approach for supervised continual learning based on approximate Bayesian inference over function space rather than the parameters of a deep neural network. We use a Gaussian process obtained by treating the weights of the last layer of a neural network as random and Gaussian distributed. Functional regularisation for continual learning naturally arises by applying the variational sparse GP inference method in a sequential fashion as new tasks are encountered. At each step of the process, a summary is constructed for the current task that consists of (i) inducing inputs and (ii) a posterior distribution over the function values at these inputs. This summary then regularises learning of future tasks, through Kullback-Leibler regularisation terms that appear in the variational lower bound, and reduces the effects of catastrophic forgetting. We fully develop the theory of the method and we demonstrate its effectiveness in classification datasets, such as Split-MNIST, Permuted-MNIST and Omniglot.

We consider the semi-supervised ordinal regression problem, where unlabeled data are given in addition to ordinal labeled data. There are many evaluation metrics in ordinal regression such as the mean absolute error, mean squared error, and mean classification error. Existing work does not take the evaluation metric into account, has a restriction on the model choice, and has no theoretical guarantee. To mitigate these problems, we propose a method based on the empirical risk minimization (ERM) framework that is applicable to optimizing all of the metrics mentioned above. Also, our method has flexible choices of models, surrogate losses, and optimization algorithms. Moreover, our method does not require a restrictive assumption on unlabeled data such as the cluster assumption and manifold assumption. We provide an estimation error bound to show that our learning method is consistent. Finally, we conduct experiments to show the usefulness of our framework.