Models, code, and papers for "Xin Tong":
Motivated by problems of anomaly detection, this paper implements the Neyman-Pearson paradigm to deal with asymmetric errors in binary classification with a convex loss. Given a finite collection of classifiers, we combine them and obtain a new classifier that satisfies simultaneously the two following properties with high probability: (i) its probability of type I error is below a pre-specified level and (ii), it has probability of type II error close to the minimum possible. The proposed classifier is obtained by solving an optimization problem with an empirical objective and an empirical constraint. New techniques to handle such problems are developed and have consequences on chance constrained programming.
Gradient descent (GD) is known to converge quickly for convex objective functions, but it can be trapped at local minimums. On the other hand, Langevin dynamics (LD) can explore the state space and find global minimums, but in order to give accurate estimates, LD needs to run with small discretization stepsize and weak stochastic force, which in general slow down its convergence. This paper shows that these two algorithms can "collaborate" through a simple exchange mechanism, in which they swap their current positions if LD yields a lower objective function. This idea can be seen as the singular limit of the replica exchange technique from the sampling literature. We show that this new algorithm converges to the global minimum linearly with high probability, assuming the objective function is strongly convex in a neighborhood of the unique global minimum. By replacing gradients with stochastic gradients, and adding a proper threshold to the exchange mechanism, our algorithm can also be used in online settings. We further verify our theoretical results through some numerical experiments, and observe superior performance of the proposed algorithm over running GD or LD alone.
We introduce a View-Volume convolutional neural network (VVNet) for inferring the occupancy and semantic labels of a volumetric 3D scene from a single depth image. The VVNet concatenates a 2D view CNN and a 3D volume CNN with a differentiable projection layer. Given a single RGBD image, our method extracts the detailed geometric features from the input depth image with a 2D view CNN and then projects the features into a 3D volume according to the input depth map via a projection layer. After that, we learn the 3D context information of the scene with a 3D volume CNN for computing the result volumetric occupancy and semantic labels. With combined 2D and 3D representations, the VVNet efficiently reduces the computational cost, enables feature extraction from multi-channel high resolution inputs, and thus significantly improves the result accuracy. We validate our method and demonstrate its efficiency and effectiveness on both synthetic SUNCG and real NYU dataset.
A common issue for classification in scientific research and industry is the existence of imbalanced classes. When sample sizes of different classes are imbalanced in training data, naively implementing a classification method often leads to unsatisfactory prediction results on test data. Multiple resampling techniques have been proposed to address the class imbalance issues. Yet, there is no general guidance on when to use each technique. In this article, we provide an objective-oriented review of the common resampling techniques for binary classification under imbalanced class sizes. The learning objectives we consider include the classical paradigm that minimizes the overall classification error, the cost-sensitive learning paradigm that minimizes a cost-adjusted weighted type I and type II errors, and the Neyman-Pearson paradigm that minimizes the type II error subject to a type I error constraint. Under each paradigm, we investigate the combination of the resampling techniques and a few state-of-the-art classification methods. For each pair of resampling techniques and classification methods, we use simulation studies to study the performance under different evaluation metrics. From these extensive simulation experiments, we demonstrate under each classification paradigm, the complex dynamics among resampling techniques, base classification methods, evaluation metrics, and imbalance ratios. For practitioners, the take-away message is that with imbalanced data, one usually should consider all the combinations of resampling techniques and the base classification methods.
Surrogate-assisted evolutionary algorithms (SAEAs) are powerful optimisation tools for computationally expensive problems (CEPs). However, a randomly selected algorithm may fail in solving unknown problems due to no free lunch theorems, and it will cause more computational resource if we re-run the algorithm or try other algorithms to get a much solution, which is more serious in CEPs. In this paper, we consider an algorithm portfolio for SAEAs to reduce the risk of choosing an inappropriate algorithm for CEPs. We propose two portfolio frameworks for very expensive problems in which the maximal number of fitness evaluations is only 5 times of the problem's dimension. One framework named Par-IBSAEA runs all algorithm candidates in parallel and a more sophisticated framework named UCB-IBSAEA employs the Upper Confidence Bound (UCB) policy from reinforcement learning to help select the most appropriate algorithm at each iteration. An effective reward definition is proposed for the UCB policy. We consider three state-of-the-art individual-based SAEAs on different problems and compare them to the portfolios built from their instances on several benchmark problems given limited computation budgets. Our experimental studies demonstrate that our proposed portfolio frameworks significantly outperform any single algorithm on the set of benchmark problems.
Rolling Horizon Evolutionary Algorithms (RHEA) are a class of online planning methods for real-time game playing; their performance is closely related to the planning horizon and the search time allowed. In this paper, we propose to learn a prior for RHEA in an offline manner by training a value network and a policy network. The value network is used to reduce the planning horizon by providing an estimation of future rewards, and the policy network is used to initialize the population, which helps to narrow down the search scope. The proposed algorithm, named prior-based RHEA (p-RHEA), trains policy and value networks by performing planning and learning iteratively. In the planning stage, the horizon-limited search assisted with the policy network and value network is performed to improve the policies and collect training samples. In the learning stage, the policy network and value network are trained with the collected samples to learn better prior knowledge. Experimental results on OpenAI Gym MuJoCo tasks show that the performance of the proposed p-RHEA is significantly improved compared to that of RHEA.
For high-dimensional classification, it is well known that naively performing the Fisher discriminant rule leads to poor results due to diverging spectra and noise accumulation. Therefore, researchers proposed independence rules to circumvent the diverse spectra, and sparse independence rules to mitigate the issue of noise accumulation. However, in biological applications, there are often a group of correlated genes responsible for clinical outcomes, and the use of the covariance information can significantly reduce misclassification rates. The extent of such error rate reductions is unveiled by comparing the misclassification rates of the Fisher discriminant rule and the independence rule. To materialize the gain based on finite samples, a Regularized Optimal Affine Discriminant (ROAD) is proposed based on a covariance penalty. ROAD selects an increasing number of features as the penalization relaxes. Further benefits can be achieved when a screening method is employed to narrow the feature pool before hitting the ROAD. An efficient Constrained Coordinate Descent algorithm (CCD) is also developed to solve the associated optimization problems. Sampling properties of oracle type are established. Simulation studies and real data analysis support our theoretical results and demonstrate the advantages of the new classification procedure under a variety of correlation structures. A delicate result on continuous piecewise linear solution path for the ROAD optimization problem at the population level justifies the linear interpolation of the CCD algorithm.
We extend Convolutional Neural Networks (CNNs) on flat and regular domains (e.g. 2D images) to curved surfaces embedded in 3D Euclidean space that are discretized as irregular meshes and widely used to represent geometric data in Computer Vision and Graphics. We define surface convolution on tangent spaces of a surface domain, where the convolution has two desirable properties: 1) the distortion of surface domain signals is locally minimal when being projected to the tangent space, and 2) the translation equi-variance property holds locally, by aligning tangent spaces with the canonical parallel transport that preserves metric. For computation, we rely on a parallel N-direction frame field on the surface that minimizes field variation and therefore is as compatible as possible to and approximates the parallel transport. On the tangent spaces equipped with parallel frames, the computation of surface convolution becomes standard routine. The frames have rotational symmetry which we disambiguate by constructing the covering space of surface induced by the parallel frames and grouping the feature maps into N sets accordingly; convolution is computed on the N branches of the cover space with respective feature maps while the kernel weights are shared. To handle irregular points of a discrete mesh while sharing kernel weights, we make the convolution semi-discrete, i.e. the convolution kernels are polynomial functions, and their convolution with discrete surface points becomes sampling and weighted summation. Pooling and unpooling operations are computed along a mesh hierarchy built through simplification. The presented surface CNNs allow effective deep learning on meshes. We show that for tasks of classification, segmentation and non-rigid registration, surface CNNs using only raw input signals achieve superior performances than previous models using sophisticated input features.
We present a new weakly supervised learning-based method for generating novel category-specific 3D shapes from unoccluded image collections. Our method is weakly supervised and only requires silhouette annotations from unoccluded, category-specific objects. Our method does not require access to the object's 3D shape, multiple observations per object from different views, intra-image pixel-correspondences, or any view annotations. Key to our method is a novel multi-projection generative adversarial network (MP-GAN) that trains a 3D shape generator to be consistent with multiple 2D projections of the 3D shapes, and without direct access to these 3D shapes. This is achieved through multiple discriminators that encode the distribution of 2D projections of the 3D shapes seen from a different views. Additionally, to determine the view information for each silhouette image, we also train a view prediction network on visualizations of 3D shapes synthesized by the generator. We iteratively alternate between training the generator and training the view prediction network. We validate our multi-projection GAN on both synthetic and real image datasets. Furthermore, we also show that multi-projection GANs can aid in learning other high-dimensional distributions from lower dimensional training datasets, such as material-class specific spatially varying reflectance properties from images.
Stochastic gradient Langevin dynamics (SGLD) is a fundamental algorithm in stochastic optimization. Recent work by Zhang et al.  presents an analysis for the hitting time of SGLD for the first and second order stationary points. The proof in Zhang et al.  is a two-stage procedure through bounding the Cheeger's constant, which is rather complicated and leads to loose bounds. In this paper, using intuitions from stochastic differential equations, we provide a direct analysis for the hitting times of SGLD to the first and second order stationary points. Our analysis is straightforward. It only relies on basic linear algebra and probability theory tools. Our direct analysis also leads to tighter bounds comparing to Zhang et al.  and shows the explicit dependence of the hitting time on different factors, including dimensionality, smoothness, noise strength, and step size effects. Under suitable conditions, we show that the hitting time of SGLD to first-order stationary points can be dimension-independent. Moreover, we apply our analysis to study several important online estimation problems in machine learning, including linear regression, matrix factorization, and online PCA.
Very expensive problems are very common in practical system that one fitness evaluation costs several hours or even days. Surrogate assisted evolutionary algorithms (SAEAs) have been widely used to solve this crucial problem in the past decades. However, most studied SAEAs focus on solving problems with a budget of at least ten times of the dimension of problems which is unacceptable in many very expensive real-world problems. In this paper, we employ Voronoi diagram to boost the performance of SAEAs and propose a novel framework named Voronoi-based efficient surrogate assisted evolutionary algorithm (VESAEA) for very expensive problems, in which the optimization budget, in terms of fitness evaluations, is only 5 times of the problem's dimension. In the proposed framework, the Voronoi diagram divides the whole search space into several subspace and then the local search is operated in some potentially better subspace. Additionally, in order to trade off the exploration and exploitation, the framework involves a global search stage developed by combining leave-one-out cross-validation and radial basis function surrogate model. A performance selector is designed to switch the search dynamically and automatically between the global and local search stages. The empirical results on a variety of benchmark problems demonstrate that the proposed framework significantly outperforms several state-of-art algorithms with extremely limited fitness evaluations. Besides, the efficacy of Voronoi-diagram is furtherly analyzed, and the results show its potential to optimize very expensive problems.
3D object reconstruction is a fundamental task of many robotics and AI problems. With the aid of deep convolutional neural networks (CNNs), 3D object reconstruction has witnessed a significant progress in recent years. However, possibly due to the prohibitively high dimension of the 3D object space, the results from deep CNNs are often prone to missing some shape details. In this paper, we present an approach which aims to preserve more shape details and improve the reconstruction quality. The key idea of our method is to leverage object mask and pose estimation from CNNs to assist the 3D shape learning by constructing a probabilistic single-view visual hull inside of the network. Our method works by first predicting a coarse shape as well as the object pose and silhouette using CNNs, followed by a novel 3D refinement CNN which refines the coarse shapes using the constructed probabilistic visual hulls. Experiment on both synthetic data and real images show that embedding a single-view visual hull for shape refinement can significantly improve the reconstruction quality by recovering more shapes details and improving shape consistency with the input image.
The Neyman-Pearson (NP) paradigm in binary classification seeks classifiers that achieve a minimal type II error while enforcing the prioritized type I error under some user-specified level. This paradigm serves naturally in applications such as severe disease diagnosis and spam detection, where people have clear priorities over the two error types. Despite recent advances in NP classification, the NP oracle inequalities, a core theoretical criterion to evaluate classifiers under the NP paradigm, were established only for classifiers based on nonparametric assumptions with bounded feature support. In this work, we conquer the challenges arisen from unbounded feature support in parametric settings and develop NP classification theory and methodology under these settings. Concretely, we propose a new parametric NP classifier NP-sLDA which satisfies the NP oracle inequalities. Furthermore, we construct an adaptive sample splitting scheme that can be applied universally to existing NP classifiers and this adaptive strategy greatly enhances the power of these classifiers. Through extensive numerical experiments and real data studies, we demonstrate the competence of NP-sLDA and the new sample splitting scheme.
Digital texts have become an increasingly important source of data for social studies. However, textual data from open platforms are vulnerable to manipulation (e.g., censorship and information inflation), often leading to bias in subsequent empirical analysis. This paper investigates the problem of data distortion in text classification when controlling type I error (a relevant textual message is classified as irrelevant) is the priority. The default classical classification paradigm that minimizes the overall classification error can yield an undesirably large type I error, and data distortion exacerbates this situation. As a solution, we propose the Neyman-Pearson (NP) classification paradigm which minimizes type II error under a user-specified type I error constraint. Theoretically, we show that while the classical oracle (i.e., optimal classifier) cannot be recovered under unknown data distortion even if one has the entire post-distortion population, the NP oracle is unaffected by data distortion and can be recovered under the same condition. Empirically, we illustrate the advantage of NP classification methods in a case study that classifies posts about strikes and corruption published on a leading Chinese blogging platform.
Most existing binary classification methods target on the optimization of the overall classification risk and may fail to serve some real-world applications such as cancer diagnosis, where users are more concerned with the risk of misclassifying one specific class than the other. Neyman-Pearson (NP) paradigm was introduced in this context as a novel statistical framework for handling asymmetric type I/II error priorities. It seeks classifiers with a minimal type II error and a constrained type I error under a user specified level. This article is the first attempt to construct classifiers with guaranteed theoretical performance under the NP paradigm in high-dimensional settings. Based on the fundamental Neyman-Pearson Lemma, we used a plug-in approach to construct NP-type classifiers for Naive Bayes models. The proposed classifiers satisfy the NP oracle inequalities, which are natural NP paradigm counterparts of the oracle inequalities in classical binary classification. Besides their desirable theoretical properties, we also demonstrated their numerical advantages in prioritized error control via both simulation and real data studies.
We propose a high dimensional classification method that involves nonparametric feature augmentation. Knowing that marginal density ratios are the most powerful univariate classifiers, we use the ratio estimates to transform the original feature measurements. Subsequently, penalized logistic regression is invoked, taking as input the newly transformed or augmented features. This procedure trains models equipped with local complexity and global simplicity, thereby avoiding the curse of dimensionality while creating a flexible nonlinear decision boundary. The resulting method is called Feature Augmentation via Nonparametrics and Selection (FANS). We motivate FANS by generalizing the Naive Bayes model, writing the log ratio of joint densities as a linear combination of those of marginal densities. It is related to generalized additive models, but has better interpretability and computability. Risk bounds are developed for FANS. In numerical analysis, FANS is compared with competing methods, so as to provide a guideline on its best application domain. Real data analysis demonstrates that FANS performs very competitively on benchmark email spam and gene expression data sets. Moreover, FANS is implemented by an extremely fast algorithm through parallel computing.
This paper addresses the problem of cross-view image based localization, where the geographic location of a ground-level street-view query image is estimated by matching it against a large scale aerial map (e.g., a high-resolution satellite image). State-of-the-art deep-learning based methods tackle this problem as deep metric learning which aims to learn global feature representations of the scene seen by the two different views. Despite promising results are obtained by such deep metric learning methods, they, however, fail to exploit a crucial cue relevant for localization, namely, the spatial layout of local features. Moreover, little attention is paid to the obvious domain gap (between aerial view and ground view) in the context of cross-view localization. This paper proposes a novel Cross-View Feature Transport (CVFT) technique to explicitly establish cross-view domain transfer that facilitates feature alignment between ground and aerial images. Specifically, we implement the CVFT as a network layer, which transports features from one domain to the other, leading to more meaningful feature similarity comparison. Our model is differentiable and can be learned end-to-end. Experiments on large-scale datasets have demonstrated that our method has remarkably boosted the state-of-the-art cross-view localization performance, e.g., on the CVUSA dataset, with significant improvements for top-1 recall from 40.79% to 61.43%, and for top-10 from 76.36% to 90.49%, compared with the previous state of the art . We expect the key insight of the paper (i.e., explicitly handling domain difference via domain transport) will prove to be useful for other similar problems in computer vision as well.