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Weiyu Li

Publications and source records attributed to Weiyu Li.

At least 37 records · Page 2Linked to original sources
arXiv2023

Example-based Motion Synthesis via Generative Motion Matching

We present GenMM, a generative model that "mines" as many diverse motions as possible from a single or few example sequences. In stark contrast to existing data-driven methods, which typically require long offline training time, are prone to visual artifacts, and tend to fail on large and complex skeletons, GenMM inherits the training-free nature and the superior quality of the well-known Motion Matching method. GenMM can synthesize a high-quality motion within a fraction of a second, even with highly complex and large skeletal structures. At the heart of our generative framework lies the generative motion matching module, which utilizes the bidirectional visual similarity as a generative cost function to motion matching, and operates in a multi-stage framework to progressively refine a random guess using exemplar motion matches. In addition to diverse motion generation, we show the versatility of our generative framework by extending it to a number of scenarios that are not possible with motion matching alone, including motion completion, key frame-guided generation, infinite looping, and motion reassembly. Code and data for this paper are at https://wyysf-98.github.io/GenMM/

cs.GR↗
arXiv2023

On the Optimal Control of Network LQR with Spatially-Exponential Decaying Structure

This paper studies network LQR problems with system matrices being spatially-exponential decaying (SED) between nodes in the network. The major objective is to study whether the optimal controller also enjoys a SED structure, which is an appealing property for ensuring the optimality of decentralized control over the network. We start with studying the open-loop asymptotically stable system and show that the optimal LQR state feedback gain $K$ is `quasi'-SED in this setting, i.e. $\|[K]_{ij}\|\sim O\left(e^{-\frac{c}{\mathrm{poly}\ln(N)}}\mathrm{dist}(i,j)\right)$. The decaying rate $c$ depends on the decaying rate and norms of system matrices and the open-loop exponential stability constants. Then the result is further generalized to unstable systems under a SED stabilizability assumption. Building upon the `quasi'-SED result on $K$, we give an upper-bound on the performance of $κ$-truncated local controllers, suggesting that distributed controllers can achieve near-optimal performance for SED systems. We develop these results via studying the structure of another type of controller, disturbance response control, which has been studied and used in recent online control literature; thus as a side result, we also prove the `quasi'-SED property of the optimal disturbance response control, which serves as a contribution on its own merit.

math.OC↗
arXiv2023

Patch-based 3D Natural Scene Generation from a Single Example

We target a 3D generative model for general natural scenes that are typically unique and intricate. Lacking the necessary volumes of training data, along with the difficulties of having ad hoc designs in presence of varying scene characteristics, renders existing setups intractable. Inspired by classical patch-based image models, we advocate for synthesizing 3D scenes at the patch level, given a single example. At the core of this work lies important algorithmic designs w.r.t the scene representation and generative patch nearest-neighbor module, that address unique challenges arising from lifting classical 2D patch-based framework to 3D generation. These design choices, on a collective level, contribute to a robust, effective, and efficient model that can generate high-quality general natural scenes with both realistic geometric structure and visual appearance, in large quantities and varieties, as demonstrated upon a variety of exemplar scenes.

cs.GR↗
arXiv2023

On the Relationship of Optimal State Feedback and Disturbance Response Controllers

This paper studies the relationship between state feedback policies and disturbance response policies for the standard Linear Quadratic Regulator (LQR). For open-loop stable plants, we establish a simple relationship between the optimal state feedback controller $u_t=K_\star x_t$ and the optimal disturbance response controller $u_t=L^{(H)}_{\star;1}w_{t-1}+\cdots+L^{(H)}_{\star;H}w_{t-H}$ with $H$-order. Here $x_t, w_t, u_t$ stands for the state, disturbance, control action of the system, respectively. Our result shows that $L_{\star,1}^{(H)}$ is a good approximation of $K_\star$ and the approximation error $\|K_\star - L_{\star,1}^{(H)}\|$ decays exponentially with $H$. We further extend this result to LQR for open-loop unstable systems, when a pre-stabilizing controller $K_0$ is available.

math.OC↗
arXiv2023

Source-Function Weighted-Transfer Learning for Nonparametric Regression with Seemingly Similar Sources

The homogeneity, or more generally, the similarity between source domains and a target domain seems to be essential to a positive transfer learning. In practice, however, the similarity condition is difficult to check and is often violated. In this paper, instead of the popularly used similarity condition, a seeming similarity is introduced, which is defined by a non-orthogonality together with a smoothness. Such a condition is naturally satisfied under common situations and even implies the dissimilarity in some sense. Based on the seeming similarity together with an $L_2$-adjustment, a source-function weighted-transfer learning estimation (sw-TLE) is constructed. By source-function weighting, an adaptive transfer learning is achieved in the sense that it is applied to similar and dissimilar scenarios with a relatively high estimation efficiency. Particularly, under the case with homogenous source and target models, the sw-TLE even can be competitive with the full data estimator. The hidden relationship between the source-function weighting estimator and the James-Stein estimator is established as well, which reveals the structural reasonability of our methodology. Moreover, the strategy does apply to nonparametric and semiparametric models. The comprehensive simulation studies and real data analysis can illustrate that the new strategy is significantly better than the competitors.

stat.ME↗
arXiv2022

Simultaneous Best Subset Selection and Dimension Reduction via Primal-Dual Iterations

Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet, their theoretical analysis is always centered on the global optimum, resulting in a discrepancy between the statistical guarantee and the numerical computation. In this research, we offer a new algorithm to address the problem and establish an almost optimal rate for the algorithmic solution. We also demonstrate that the algorithm achieves the estimation with a polynomial number of iterations. In addition, we present a generalized information criterion to simultaneously ensure the consistency of support set recovery and rank estimation. Under the proposed criterion, we show that our algorithm can achieve the oracle reduced rank estimation with a significant probability. The numerical studies and an application in the ovarian cancer genetic data demonstrate the effectiveness and scalability of our approach.

stat.ME↗
arXiv2022

A Correlation-Ratio Transfer Learning and Variational Stein's Paradox

A basic condition for efficient transfer learning is the similarity between a target model and source models. In practice, however, the similarity condition is difficult to meet or is even violated. Instead of the similarity condition, a brand-new strategy, linear correlation-ratio, is introduced in this paper to build an accurate relationship between the models. Such a correlation-ratio can be easily estimated by historical data or a part of sample. Then, a correlation-ratio transfer learning likelihood is established based on the correlation-ratio combination. On the practical side, the new framework is applied to some application scenarios, especially the areas of data streams and medical studies. Methodologically, some techniques are suggested for transferring the information from simple source models to a relatively complex target model. Theoretically, some favorable properties, including the global convergence rate, are achieved, even for the case where the source models are not similar to the target model. All in all, it can be seen from the theories and experimental results that the inference on the target model is significantly improved by the information from similar or dissimilar source models. In other words, a variational Stein's paradox is illustrated in the context of transfer learning.

stat.ML↗
arXiv2022

Ternary and Binary Quantization for Improved Classification

Dimension reduction and data quantization are two important methods for reducing data complexity. In the paper, we study the methodology of first reducing data dimension by random projection and then quantizing the projections to ternary or binary codes, which has been widely applied in classification. Usually, the quantization will seriously degrade the accuracy of classification due to high quantization errors. Interestingly, however, we observe that the quantization could provide comparable and often superior accuracy, as the data to be quantized are sparse features generated with common filters. Furthermore, this quantization property could be maintained in the random projections of sparse features, if both the features and random projection matrices are sufficiently sparse. By conducting extensive experiments, we validate and analyze this intriguing property.

cs.CV↗
arXiv2022

MoCo-Flow: Neural Motion Consensus Flow for Dynamic Humans in Stationary Monocular Cameras

Synthesizing novel views of dynamic humans from stationary monocular cameras is a specialized but desirable setup. This is particularly attractive as it does not require static scenes, controlled environments, or specialized capture hardware. In contrast to techniques that exploit multi-view observations, the problem of modeling a dynamic scene from a single view is significantly more under-constrained and ill-posed. In this paper, we introduce Neural Motion Consensus Flow (MoCo-Flow), a representation that models dynamic humans in stationary monocular cameras using a 4D continuous time-variant function. We learn the proposed representation by optimizing for a dynamic scene that minimizes the total rendering error, over all the observed images. At the heart of our work lies a carefully designed optimization scheme, which includes a dedicated initialization step and is constrained by a motion consensus regularization on the estimated motion flow. We extensively evaluate MoCo-Flow on several datasets that contain human motions of varying complexity, and compare, both qualitatively and quantitatively, to several baselines and ablated variations of our methods, showing the efficacy and merits of the proposed approach. Pretrained model, code, and data will be released for research purposes upon paper acceptance.

cs.CV↗
arXiv2021

Cascaded Compressed Sensing Networks: A Reversible Architecture for Layerwise Learning

Recently, the method that learns networks layer by layer has attracted increasing interest for its ease of analysis. For the method, the main challenge lies in deriving an optimization target for each layer by inversely propagating the global target of the network. The propagation problem is ill posed, due to involving the inversion of nonlinear activations from lowdimensional to high-dimensional spaces. To address the problem, the existing solution is to learn an auxiliary network to specially propagate the target. However, the network lacks stability, and moreover, it results in higher complexity for network learning. In the letter, we show that target propagation could be achieved by modeling the network s each layer with compressed sensing, without the need of auxiliary networks. Experiments show that the proposed method could achieve better performance than the auxiliary network-based method.

cs.LG↗
arXiv2021

Deep Learning to Ternary Hash Codes by Continuation

Recently, it has been observed that {0,1,-1}-ternary codes which are simply generated from deep features by hard thresholding, tend to outperform {-1,1}-binary codes in image retrieval. To obtain better ternary codes, we for the first time propose to jointly learn the features with the codes by appending a smoothed function to the networks. During training, the function could evolve into a non-smoothed ternary function by a continuation method. The method circumvents the difficulty of directly training discrete functions and reduces the quantization errors of ternary codes. Experiments show that the generated codes indeed could achieve higher retrieval accuracy.

cs.CV↗
arXiv2021

Stochastic Alternating Direction Method of Multipliers for Byzantine-Robust Distributed Learning

This paper aims to solve a distributed learning problem under Byzantine attacks. In the underlying distributed system, a number of unknown but malicious workers (termed as Byzantine workers) can send arbitrary messages to the master and bias the learning process, due to data corruptions, computation errors or malicious attacks. Prior work has considered a total variation (TV) norm-penalized approximation formulation to handle the Byzantine attacks, where the TV norm penalty forces the regular workers' local variables to be close, and meanwhile, tolerates the outliers sent by the Byzantine workers. To solve the TV norm-penalized approximation formulation, we propose a Byzantine-robust stochastic alternating direction method of multipliers (ADMM) that fully utilizes the separable problem structure. Theoretically, we prove that the proposed method converges to a bounded neighborhood of the optimal solution at a rate of O(1/k) under mild assumptions, where k is the number of iterations and the size of neighborhood is determined by the number of Byzantine workers. Numerical experiments on the MNIST and COVERTYPE datasets demonstrate the effectiveness of the proposed method to various Byzantine attacks.

math.OC↗
arXiv2020

Byzantine-Robust Decentralized Stochastic Optimization over Static and Time-Varying Networks

In this paper, we consider the Byzantine-robust stochastic optimization problem defined over decentralized static and time-varying networks, where the agents collaboratively minimize the summation of expectations of stochastic local cost functions, but some of the agents are unreliable due to data corruptions, equipment failures or cyber-attacks. The unreliable agents, which are called as Byzantine agents thereafter, can send faulty values to their neighbors and bias the optimization process. Our key idea to handle the Byzantine attacks is to formulate a total variation (TV) norm-penalized approximation of the Byzantine-free problem, where the penalty term forces the local models of regular agents to be close, but also allows the existence of outliers from the Byzantine agents. A stochastic subgradient method is applied to solve the penalized problem. We prove that the proposed method reaches a neighborhood of the Byzantine-free optimal solution, and the size of neighborhood is determined by the number of Byzantine agents and the network topology. Numerical experiments corroborate the theoretical analysis, as well as demonstrate the robustness of the proposed method to Byzantine attacks and its superior performance comparing to existing methods.

math.OC↗
arXiv2020

Unified Rules of Renewable Weighted Sums for Various Online Updating Estimations

This paper establishes unified frameworks of renewable weighted sums (RWS) for various online updating estimations in the models with streaming data sets. The newly defined RWS lays the foundation of online updating likelihood, online updating loss function, online updating estimating equation and so on. The idea of RWS is intuitive and heuristic, and the algorithm is computationally simple. This paper chooses nonparametric model as an exemplary setting. The RWS applies to various types of nonparametric estimators, which include but are not limited to nonparametric likelihood, quasi-likelihood and least squares. Furthermore, the method and the theory can be extended into the models with both parameter and nonparametric function. The estimation consistency and asymptotic normality of the proposed renewable estimator are established, and the oracle property is obtained. Moreover, these properties are always satisfied, without any constraint on the number of data batches, which means that the new method is adaptive to the situation where streaming data sets arrive perpetually. The behavior of the method is further illustrated by various numerical examples from simulation experiments and real data analysis.

stat.ME↗
arXiv2020

Communication-Censored Distributed Stochastic Gradient Descent

This paper develops a communication-efficient algorithm to solve the stochastic optimization problem defined over a distributed network, aiming at reducing the burdensome communication in applications such as distributed machine learning.Different from the existing works based on quantization and sparsification, we introduce a communication-censoring technique to reduce the transmissions of variables, which leads to our communication-Censored distributed Stochastic Gradient Descent (CSGD) algorithm. Specifically, in CSGD, the latest mini-batch stochastic gradient at a worker will be transmitted to the server if and only if it is sufficiently informative. When the latest gradient is not available, the stale one will be reused at the server. To implement this communication-censoring strategy, the batch-size is increasing in order to alleviate the effect of stochastic gradient noise. Theoretically, CSGD enjoys the same order of convergence rate as that of SGD, but effectively reduces communication. Numerical experiments demonstrate the sizable communication saving of CSGD.

stat.ML↗
arXiv2019

Communication-Censored Linearized ADMM for Decentralized Consensus Optimization

In this paper, we propose a communication- and computation-efficient algorithm to solve a convex consensus optimization problem defined over a decentralized network. A remarkable existing algorithm to solve this problem is the alternating direction method of multipliers (ADMM), in which at every iteration every node updates its local variable through combining neighboring variables and solving an optimization subproblem. The proposed algorithm, called as COmmunication-censored Linearized ADMM (COLA), leverages a linearization technique to reduce the iteration-wise computation cost of ADMM and uses a communication-censoring strategy to alleviate the communication cost. To be specific, COLA introduces successive linearization approximations to the local cost functions such that the resultant computation is first-order and light-weight. Since the linearization technique slows down the convergence speed, COLA further adopts the communication-censoring strategy to avoid transmissions of less informative messages. A node is allowed to transmit only if the distance between the current local variable and its previously transmitted one is larger than a censoring threshold. COLA is proven to be convergent when the local cost functions have Lipschitz continuous gradients and the censoring threshold is summable. When the local cost functions are further strongly convex, we establish the linear (sublinear) convergence rate of COLA, given that the censoring threshold linearly (sublinearly) decays to 0. Numerical experiments corroborate with the theoretical findings and demonstrate the satisfactory communication-computation tradeoff of COLA.

math.OC↗
arXiv2017

A semiparametric single-index estimator for a class of estimating equation models

We propose a two-step pseudo-maximum likelihood procedure for semiparametric single-index regression models where the conditional variance is a known function of the regression and an additional parameter. The Poisson single-index regression with multiplicative unobserved heterogeneity is an example of such models. Our procedure is based on linear exponential densities with nuisance parameter. The pseudo-likelihood criterion we use contains a nonparametric estimate of the index regression and therefore a rule for choosing the smoothing parameter is needed. We propose an automatic and natural rule based on the joint maximization of the pseudo-likelihood with respect to the index parameter and the smoothing parameter. We derive the asymptotic properties of the semiparametric estimator of the index parameter and the asymptotic behavior of our `optimal' smoothing parameter. The finite sample performances of our methodology are analyzed using simulated and real data.

math.ST↗