Regressive Domain Adaptation for Unsupervised Keypoint Detection

Domain adaptation (DA) aims at transferring knowledge from a labeled source domain to an unlabeled target domain. Though many DA theories and algorithms have been proposed, most of them are tailored into classification settings and may fail in regression tasks, especially in the practical keypoint detection task. To tackle this difficult but significant task, we present a method of regressive domain adaptation (RegDA) for unsupervised keypoint detection. Inspired by the latest theoretical work, we first utilize an adversarial regressor to maximize the disparity on the target domain and train a feature generator to minimize this disparity. However, due to the high dimension of the output space, this regressor fails to detect samples that deviate from the support of the source. To overcome this problem, we propose two important ideas. First, based on our observation that the probability density of the output space is sparse, we introduce a spatial probability distribution to describe this sparsity and then use it to guide the learning of the adversarial regressor. Second, to alleviate the optimization difficulty in the high-dimensional space, we innovatively convert the minimax game in the adversarial training to the minimization of two opposite goals. Extensive experiments show that our method brings large improvement by 8% to 11% in terms of PCK on different datasets.

Camera-Space Hand Mesh Recovery via Semantic Aggregation and Adaptive 2D-1D Registration

Recent years have witnessed significant progress in 3D hand mesh recovery. Nevertheless, because of the intrinsic 2D-to-3D ambiguity, recovering camera-space 3D information from a single RGB image remains challenging. To tackle this problem, we divide camera-space mesh recovery into two sub-tasks, i.e., root-relative mesh recovery and root recovery. First, joint landmarks and silhouette are extracted from a single input image to provide 2D cues for the 3D tasks. In the root-relative mesh recovery task, we exploit semantic relations among joints to generate a 3D mesh from the extracted 2D cues. Such generated 3D mesh coordinates are expressed relative to a root position, i.e., wrist of the hand. In the root recovery task, the root position is registered to the camera space by aligning the generated 3D mesh back to 2D cues, thereby completing camera-space 3D mesh recovery. Our pipeline is novel in that (1) it explicitly makes use of known semantic relations among joints and (2) it exploits 1D projections of the silhouette and mesh to achieve robust registration. Extensive experiments on popular datasets such as FreiHAND, RHD, and Human3.6M demonstrate that our approach achieves state-of-the-art performance on both root-relative mesh recovery and root recovery. Our code is publicly available at https://github.com/SeanChenxy/HandMesh.

Learning Optimal Distributionally Robust Individualized Treatment Rules

Recent development in the data-driven decision science has seen great advances in individualized decision making. Given data with individual covariates, treatment assignments and outcomes, policy makers best individualized treatment rule (ITR) that maximizes the expected outcome, known as the value function. Many existing methods assume that the training and testing distributions are the same. However, the estimated optimal ITR may have poor generalizability when the training and testing distributions are not identical. In this paper, we consider the problem of finding an optimal ITR from a restricted ITR class where there is some unknown covariate changes between the training and testing distributions. We propose a novel distributionally robust ITR (DR-ITR) framework that maximizes the worst-case value function across the values under a set of underlying distributions that are "close" to the training distribution. The resulting DR-ITR can guarantee the performance among all such distributions reasonably well. We further propose a calibrating procedure that tunes the DR-ITR adaptively to a small amount of calibration data from a target population. In this way, the calibrated DR-ITR can be shown to enjoy better generalizability than the standard ITR based on our numerical studies.

High dimensional precision medicine from patient-derived xenografts

The complexity of human cancer often results in significant heterogeneity in response to treatment. Precision medicine offers potential to improve patient outcomes by leveraging this heterogeneity. Individualized treatment rules (ITRs) formalize precision medicine as maps from the patient covariate space into the space of allowable treatments. The optimal ITR is that which maximizes the mean of a clinical outcome in a population of interest. Patient-derived xenograft (PDX) studies permit the evaluation of multiple treatments within a single tumor and thus are ideally suited for estimating optimal ITRs. PDX data are characterized by correlated outcomes, a high-dimensional feature space, and a large number of treatments. Existing methods for estimating optimal ITRs do not take advantage of the unique structure of PDX data or handle the associated challenges well. In this paper, we explore machine learning methods for estimating optimal ITRs from PDX data. We analyze data from a large PDX study to identify biomarkers that are informative for developing personalized treatment recommendations in multiple cancers. We estimate optimal ITRs using regression-based approaches such as Q-learning and direct search methods such as outcome weighted learning. Finally, we implement a superlearner approach to combine a set of estimated ITRs and show that the resulting ITR performs better than any of the input ITRs, mitigating uncertainty regarding user choice of any particular ITR estimation methodology. Our results indicate that PDX data are a valuable resource for developing individualized treatment strategies in oncology.

Statistical Analysis of Stationary Solutions of Coupled Nonconvex Nonsmooth Empirical Risk Minimization

This paper has two main goals: (a) establish several statistical properties---consistency, asymptotic distributions, and convergence rates---of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk minimization problems, and (b) validate these properties by a noisy amplitude-based phase retrieval problem, the latter being of much topical interest.Derived from available data via sampling, these empirical risk minimization problems are the computational workhorse of a population risk model which involves the minimization of an expected value of a random functional. When these minimization problems are nonconvex, the computation of their globally optimal solutions is elusive. Together with the fact that the expectation operator cannot be evaluated for general probability distributions, it becomes necessary to justify whether the stationary solutions of the empirical problems are practical approximations of the stationary solution of the population problem. When these two features, general distribution and nonconvexity, are coupled with nondifferentiability that often renders the problems "non-Clarke regular", the task of the justification becomes challenging. Our work aims to address such a challenge within an algorithm-free setting. The resulting analysis is therefore different from the much of the analysis in the recent literature that is based on local search algorithms. Furthermore, supplementing the classical minimizer-centric analysis, our results offer a first step to close the gap between computational optimization and asymptotic analysis of coupled nonconvex nonsmooth statistical estimation problems, expanding the former with statistical properties of the practically obtained solution and providing the latter with a more practical focus pertaining to computational tractability.

Adaptive Wasserstein Hourglass for Weakly Supervised Hand Pose Estimation from Monocular RGB

Insufficient labeled training datasets is one of the bottlenecks of 3D hand pose estimation from monocular RGB images. Synthetic datasets have a large number of images with precise annotations, but the obvious difference with real-world datasets impacts the generalization. Little work has been done to bridge the gap between two domains over their wide difference. In this paper, we propose a domain adaptation method called Adaptive Wasserstein Hourglass (AW Hourglass) for weakly-supervised 3D hand pose estimation, which aims to distinguish the difference and explore the common characteristics (e.g. hand structure) of synthetic and real-world datasets. Learning the common characteristics helps the network focus on pose-related information. The similarity of the characteristics makes it easier to enforce domain-invariant constraints. During training, based on the relation between these common characteristics and 3D pose learned from fully-annotated synthetic datasets, it is beneficial for the network to restore the 3D pose of weakly labeled real-world datasets with the aid of 2D annotations and depth images. While in testing, the network predicts the 3D pose with the input of RGB.

Estimation of Individualized Decision Rules Based on an Optimized Covariate-Dependent Equivalent of Random Outcomes

Recent exploration of optimal individualized decision rules (IDRs) for patients in precision medicine has attracted a lot of attention due to the heterogeneous responses of patients to different treatments. In the existing literature of precision medicine, an optimal IDR is defined as a decision function mapping from the patients' covariate space into the treatment space that maximizes the expected outcome of each individual. Motivated by the concept of Optimized Certainty Equivalent (OCE) introduced originally in \cite{ben1986expected} that includes the popular conditional-value-of risk (CVaR) \cite{rockafellar2000optimization}, we propose a decision-rule based optimized covariates dependent equivalent (CDE) for individualized decision making problems. Our proposed IDR-CDE broadens the existing expected-mean outcome framework in precision medicine and enriches the previous concept of the OCE. Numerical experiments demonstrate that our overall approach outperforms existing methods in estimating optimal IDRs under heavy-tail distributions of the data.

Simultaneous Clustering and Estimation of Heterogeneous Graphical Models

We consider joint estimation of multiple graphical models arising from heterogeneous and high-dimensional observations. Unlike most previous approaches which assume that the cluster structure is given in advance, an appealing feature of our method is to learn cluster structure while estimating heterogeneous graphical models. This is achieved via a high dimensional version of Expectation Conditional Maximization (ECM) algorithm (Meng and Rubin, 1993). A joint graphical lasso penalty is imposed on the conditional maximization step to extract both homogeneity and heterogeneity components across all clusters. Our algorithm is computationally efficient due to fast sparse learning routines and can be implemented without unsupervised learning knowledge. The superior performance of our method is demonstrated by extensive experiments and its application to a Glioblastoma cancer dataset reveals some new insights in understanding the Glioblastoma cancer. In theory, a non-asymptotic error bound is established for the output directly from our high dimensional ECM algorithm, and it consists of two quantities: statistical error (statistical accuracy) and optimization error (computational complexity). Such a result gives a theoretical guideline in terminating our ECM iterations.

Stability Enhanced Large-Margin Classifier Selection

Stability is an important aspect of a classification procedure because unstable predictions can potentially reduce users' trust in a classification system and also harm the reproducibility of scientific conclusions. The major goal of our work is to introduce a novel concept of classification instability, i.e., decision boundary instability (DBI), and incorporate it with the generalization error (GE) as a standard for selecting the most accurate and stable classifier. Specifically, we implement a two-stage algorithm: (i) initially select a subset of classifiers whose estimated GEs are not significantly different from the minimal estimated GE among all the candidate classifiers; (ii) the optimal classifier is chosen as the one achieving the minimal DBI among the subset selected in stage (i). This general selection principle applies to both linear and nonlinear classifiers. Large-margin classifiers are used as a prototypical example to illustrate the above idea. Our selection method is shown to be consistent in the sense that the optimal classifier simultaneously achieves the minimal GE and the minimal DBI. Various simulations and real examples further demonstrate the advantage of our method over several alternative approaches.

Joint Estimation of Multiple Dependent Gaussian Graphical Models with Applications to Mouse Genomics

Gaussian graphical models are widely used to represent conditional dependence among random variables. In this paper, we propose a novel estimator for data arising from a group of Gaussian graphical models that are themselves dependent. A motivating example is that of modeling gene expression collected on multiple tissues from the same individual: here the multivariate outcome is affected by dependencies acting not only at the level of the specific tissues, but also at the level of the whole body; existing methods that assume independence among graphs are not applicable in this case. To estimate multiple dependent graphs, we decompose the problem into two graphical layers: the systemic layer, which affects all outcomes and thereby induces cross- graph dependence, and the category-specific layer, which represents graph-specific variation. We propose a graphical EM technique that estimates both layers jointly, establish estimation consistency and selection sparsistency of the proposed estimator, and confirm by simulation that the EM method is superior to a simple one-step method. We apply our technique to mouse genomics data and obtain biologically plausible results.