The accurate prediction of molecular energetics in chemical compound space is a crucial ingredient for rational compound design. The inherently graph-like, non-vectorial nature of molecular data gives rise to a unique and difficult machine learning problem. In this paper, we adopt a learning-from-scratch approach where quantum-mechanical molecular energies are predicted directly from the raw molecular geometry. The study suggests a benefit from setting flexible priors and enforcing invariance stochastically rather than structurally. Our results improve the state-of-the-art by a factor of almost three, bringing statistical methods one step closer to the holy grail of ''chemical accuracy''.

In this paper we introduce Context-Sensitive Decision Forests - A new perspective to exploit contextual information in the popular decision forest framework for the object detection problem. They are tree-structured classifiers with the ability to access intermediate prediction (here: classification and regression) information during training and inference time. This intermediate prediction is available to each sample, which allows us to develop context-based decision criteria, used for refining the prediction process. In addition, we introduce a novel split criterion which in combination with a priority based way of constructing the trees, allows more accurate regression mode selection and hence improves the current context information. In our experiments, we demonstrate improved results for the task of pedestrian detection on the challenging TUD data set when compared to state-of-the-art methods.

We present a truncation-free online variational inference algorithm for Bayesian nonparametric models. Unlike traditional (online) variational inference algorithms that require truncations for the model or the variational distribution, our method adapts model complexity on the fly. Our experiments for Dirichlet process mixture models and hierarchical Dirichlet process topic models on two large-scale data sets show better performance than previous online variational inference algorithms.

This paper presents a novel non-parametric approximate dynamic programming (ADP) algorithm that enjoys graceful, dimension-independent approximation and sample complexity guarantees. In particular, we establish both theoretically and computationally that our proposal can serve as a viable alternative to state-of-the-art parametric ADP algorithms, freeing the designer from carefully specifying an approximation architecture. We accomplish this by developing a kernel-based mathematical program for ADP. Via a computational study on a controlled queueing network, we show that our non-parametric procedure is competitive with parametric ADP approaches.

We present a novel approach to low-level vision problems that combines sparse coding and deep networks pre-trained with denoising auto-encoder (DA). We propose analternative training scheme that successfully adapts DA, originally designed forunsupervised feature learning, to the tasks of image denoising and blind inpainting. Our method's performance in the image denoising task is comparable to that of KSVD which is a widely used sparse coding technique. More importantly, inblind image inpainting task, the proposed method provides solutions to some complex problems that have not been tackled before. Specifically, we can automatically remove complex patterns like superimposed text from an image, rather than simple patterns like pixels missing at random. Moreover, the proposed method does not need the information regarding the region that requires inpainting tobe given a priori. Experimental results demonstrate the effectiveness of the proposed method in the tasks of image denoising and blind inpainting. We also show that our new training scheme for DA is more effective and can improve the performance of unsupervised feature learning.

In many practical machine learning problems, the acquisition of labeled data is often expensive and/or time consuming. This motivates us to study a problem as follows: given a label budget, how to select data points to label such that the learning performance is optimized. We propose a selective labeling method by analyzing the generalization error of Laplacian regularized Least Squares (LapRLS). In particular, we derive a deterministic generalization error bound for LapRLS trained on subsampled data, and propose to select a subset of data points to label by minimizing this upper bound. Since the minimization is a combinational problem, we relax it into continuous domain and solve it by projected gradient descent. Experiments on benchmark datasets show that the proposed method outperforms the state-of-the-art methods.

While long term human visual memory can store a remarkable amount of visual information, it tends to degrade over time. Recent works have shown that image memorability is an intrinsic property of an image that can be reliably estimated using state-of-the-art image features and machine learning algorithms. However, the class of features and image information that is forgotten has not been explored yet. In this work, we propose a probabilistic framework that models how and which local regions from an image may be forgotten using a data-driven approach that combines local and global images features. The model automatically discovers memorabilitymaps of individual images without any human annotation. We incorporate multiple image region attributes in our algorithm, leading to improved memorability prediction of images as compared to previous works.

Multi-task learning (MTL) aims to improve generalization performance by learning multiple related tasks simultaneously and identifying the shared information among tasks. Most of existing MTL methods focus on learning linear models under the supervised setting. We propose a novel semi-supervised and nonlinear approach for MTL using vector fields. A vector field is a smooth mapping from the manifold to the tangent spaces which can be viewed as a directional derivative of functions on the manifold. We argue that vector fields provide a natural way to exploit the geometric structure of data as well as the shared differential structure of tasks, both are crucial for semi-supervised multi-task learning. In this paper, we develop multi-task vector field learning (MTVFL) which learns the prediction functions and the vector fields simultaneously. MTVFL has the following key properties: (1) the vector fields we learned are close to the gradient fields of the prediction functions; (2) within each task, the vector field is required to be as parallel as possible which is expected to span a low dimensional subspace; (3) the vector fields from all tasks share a low dimensional subspace. We formalize our idea in a regularization framework and also provide a convex relaxation method to solve the original non-convex problem. The experimental results on synthetic and real data demonstrate the effectiveness of our proposed approach.

In this paper, a novel, computationally fast, and alternative algorithm for com- puting weighted v-statistics in resampling both univariate and multivariate data is proposed. To avoid any real resampling, we have linked this problem with finite group action and converted it into a problem of orbit enumeration. For further computational cost reduction, an efficient method is developed to list all orbits by their symmetry order and calculate all index function orbit sums and data function orbit sums recursively. The computational complexity analysis shows reduction in the computational cost from n! or nn level to low-order polynomial level.

We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where the function oscillates more, while allocating the samples such that they are well spread on the domain (this notion shares similitude with low discrepancy). We prove that the estimate returned by the algorithm is almost as accurate as the estimate that an optimal oracle strategy (that would know the variations of the function everywhere) would return, and we provide a finite-sample analysis.