We propose an accelerated-gradient-based MCMC method. It relies on a modification of the Nesterov's accelerated gradient method for strongly convex functions (NAG-SC): We first reformulate NAG-SC as a Hessian-Free High-Resolution ODE, then release the high-resolution coefficient as a free hyperparameter, and finally inject appropriate noise and discretize the diffusion process. Accelerated sampling enabled by this new hyperparameter is not only experimentally demonstrated on several learning tasks, but also theoretically quantified, both at the continuous level and after discretization. For (not-necessarily-strongly-) convex and $L$-smooth potentials, exponential convergence in $\chi^2$ divergence is proved, with a rate analogous to state-of-the-art results of underdamped Langevin dynamics, plus an additional acceleration. At the same time, the method also works for nonconvex potentials, for which we also establish exponential convergence as long as the potential satisfies a Poincar\'e inequality.

We study without-replacement SGD for solving finite-sum optimization problems. Specifically, depending on how the indices of the finite-sum are shuffled, we consider the RandomShuffle (shuffle at the beginning of each epoch) and SingleShuffle (shuffle only once) algorithms. First, we establish minimax optimal convergence rates of these algorithms up to poly-log factors. Notably, our analysis is general enough to cover gradient dominated nonconvex costs, and does not rely on the convexity of individual component functions unlike existing optimal convergence results. Secondly, assuming convexity of the individual components, we further sharpen the tight convergence results for RandomShuffle by removing the drawbacks common to all prior arts: large number of epochs required for the results to hold, and extra poly-log factor gaps to the lower bound.

Zeroth-order (ZO) optimization is a subset of gradient-free optimization that emerges in many signal processing and machine learning applications. It is used for solving optimization problems similarly to gradient-based methods. However, it does not require the gradient, using only function evaluations. Specifically, ZO optimization iteratively performs three major steps: gradient estimation, descent direction computation, and solution update. In this paper, we provide a comprehensive review of ZO optimization, with an emphasis on showing the underlying intuition, optimization principles and recent advances in convergence analysis. Moreover, we demonstrate promising applications of ZO optimization, such as evaluating robustness and generating explanations from black-box deep learning models, and efficient online sensor management.

The model uncertainty obtained by variational Bayesian inference with Monte Carlo dropout is prone to miscalibration. In this paper, different logit scaling methods are extended to dropout variational inference to recalibrate model uncertainty. Expected uncertainty calibration error (UCE) is presented as a metric to measure miscalibration. The effectiveness of recalibration is evaluated on CIFAR-10/100 and SVHN for recent CNN architectures. Experimental results show that logit scaling considerably reduce miscalibration by means of UCE. Well-calibrated uncertainty enables reliable rejection of uncertain predictions and robust detection of out-of-distribution data.

System identification is a key step for model-based control, estimator design, and output prediction. This work considers the offline identification of partially observed nonlinear systems. We empirically show that the certainty-equivalent approximation to expectation-maximization can be a reliable and scalable approach for high-dimensional deterministic systems, which are common in robotics. We formulate certainty-equivalent expectation-maximization as block coordinate-ascent, and provide an efficient implementation. The algorithm is tested on a simulated system of coupled Lorenz attractors, demonstrating its ability to identify high-dimensional systems that can be intractable for particle-based approaches. Our approach is also used to identify the dynamics of an aerobatic helicopter. By augmenting the state with unobserved fluid states, a model is learned that predicts the acceleration of the helicopter better than state-of-the-art approaches. The codebase for this work is available at https://github.com/sisl/CEEM.

Constraint Optimization Problems (COP) are often considered without sufficient knowledge on the boundaries of the objective variable to optimize. When available, tight boundaries are helpful to prune the search space or estimate problem characteristics. Finding close boundaries, that correctly under- and overestimate the optimum, is almost impossible without actually solving the COP. This paper introduces Bion, a novel approach for boundary estimation by learning from previously solved instances of the COP. Based on supervised machine learning, Bion is problem-specific and solver-independent and can be applied to any COP which is repeatedly solved with different data inputs. An experimental evaluation over seven realistic COPs shows that an estimation model can be trained to prune the objective variables' domains by over 80%. By evaluating the estimated boundaries with various COP solvers, we find that Bion improves the solving process for some problems, although the effect of closer bounds is generally problem-dependent.

The central goal of this paper is to establish two commonly available dimensionality reduction (DR) methods i.e. t-distributed Stochastic Neighbor Embedding (t-SNE) and Multidimensional Scaling (MDS) in Matlab and to observe their application in several datasets. These DR techniques are applied to nine different datasets namely CNAE9, Segmentation, Seeds, Pima Indians diabetes, Parkinsons, Movement Libras, Mammographic Masses, Knowledge, and Ionosphere acquired from UCI machine learning repository. By applying t-SNE and MDS algorithms, each dataset is transformed to the half of its original dimension by eliminating unnecessary features from the datasets. Subsequently, these datasets with reduced dimensions are fed into three supervised classification algorithms for classification. These classification algorithms are K Nearest Neighbors (KNN), Extended Nearest Neighbors (ENN), and Support Vector Machine (SVM). Again, all these algorithms are implemented in Matlab. The training and test data ratios are maintained as ninety percent: ten percent for each dataset. Upon accuracy observation, the efficiency for every dimensionality technique with availed classification algorithms is analyzed and the performance of each classifier is evaluated.

An interesting development in automatic visual recognition has been the emergence of tasks where it is not possible to assign ground truth labels to images, yet still feasible to collect annotations that reflect human judgements about them. Such tasks include subjective visual attribute assignment and the labeling of ambiguous scenes. Machine learning-based predictors for these tasks rely on supervised training that models the behavior of the annotators, e.g., what would the average person's judgement be for an image? A key open question for this type of work, especially for applications where inconsistency with human behavior can lead to ethical lapses, is how to evaluate the uncertainty of trained predictors. Given that the real answer is unknowable, we are left with often noisy judgements from human annotators to work with. In order to account for the uncertainty that is present, we propose a relative Bayesian framework for evaluating predictors trained on such data. The framework specifies how to estimate a predictor's uncertainty due to the human labels by approximating a conditional distribution and producing a credible interval for the predictions and their measures of performance. The framework is successfully applied to four image classification tasks that use subjective human judgements: facial beauty assessment using the SCUT-FBP5500 dataset, social attribute assignment using data from TestMyBrain.org,

Inverse reinforcement learning (IRL) aims to estimate the reward function of optimizing agents by observing their response (estimates or actions). This paper considers IRL when noisy estimates of the gradient of a reward function generated by multiple stochastic gradient agents are observed. We present a generalized Langevin dynamics algorithm to estimate the reward function $R(\theta)$; specifically, the resulting Langevin algorithm asymptotically generates samples from the distribution proportional to $\exp(R(\theta))$. The proposed IRL algorithms use kernel-based passive learning schemes. We also construct multi-kernel passive Langevin algorithms for IRL which are suitable for high dimensional data. The performance of the proposed IRL algorithms are illustrated on examples in adaptive Bayesian learning, logistic regression (high dimensional problem) and constrained Markov decision processes. We prove weak convergence of the proposed IRL algorithms using martingale averaging methods. We also analyze the tracking performance of the IRL algorithms in non-stationary environments where the utility function $R(\theta)$ jump changes over time as a slow Markov chain.

Accurate real-time traffic forecasting is a core technological problem against the implementation of the intelligent transportation system. However, it remains challenging considering the complex spatial and temporal dependencies among traffic flows. In the spatial dimension, due to the connectivity of the road network, the traffic flows between linked roads are closely related. In terms of the temporal factor, although there exists a tendency among adjacent time points in general, the importance of distant past points is not necessarily smaller than that of recent past points since traffic flows are also affected by external factors. In this study, an attention temporal graph convolutional network (A3T-GCN) traffic forecasting method was proposed to simultaneously capture global temporal dynamics and spatial correlations. The A3T-GCN model learns the short-time trend in time series by using the gated recurrent units and learns the spatial dependence based on the topology of the road network through the graph convolutional network. Moreover, the attention mechanism was introduced to adjust the importance of different time points and assemble global temporal information to improve prediction accuracy. Experimental results in real-world datasets demonstrate the effectiveness and robustness of proposed A3T-GCN. The source code can be visited at https://github.com/lehaifeng/T-GCN/A3T.