Haitao Liu

Xinpeng Ling, Jie Fu, Kuncan Wang et al.

Federated Learning (FL) is a distributed machine learning technique that allows model training among multiple devices or organizations by sharing training parameters instead of raw data. However, adversaries can still infer individual information through inference attacks (e.g. differential attacks) on these training parameters. As a result, Differential Privacy (DP) has been widely used in FL to prevent such attacks. We consider differentially private federated learning in a resource-constrained scenario, where both privacy budget and communication rounds are constrained. By theoretically analyzing the convergence, we can find the optimal number of local DPSGD iterations for clients between any two sequential global updates. Based on this, we design an algorithm of Differentially Private Federated Learning with Adaptive Local Iterations (ALI-DPFL). We experiment our algorithm on the MNIST, FashionMNIST and Cifar10 datasets, and demonstrate significantly better performances than previous work in the resource-constraint scenario. Code is available at https://github.com/cheng-t/ALI-DPFL.

Yugeng Huang, Haitao Liu, Tian Huang

As an efficient algorithm to solve the multi-view registration problem,the motion averaging (MA) algorithm has been extensively studied and many MA-based algorithms have been introduced. They aim at recovering global motions from relative motions and exploiting information redundancy to average accumulative errors. However, one property of these methods is that they use Guass-Newton method to solve a least squares problem for the increment of global motions, which may lead to low efficiency and poor robustness to outliers. In this paper, we propose a novel motion averaging framework for the multi-view registration with Laplacian kernel-based maximum correntropy criterion (LMCC). Utilizing the Lie algebra motion framework and the correntropy measure, we propose a new cost function that takes all constraints supplied by relative motions into account. Obtaining the increment used to correct the global motions, can further be formulated as an optimization problem aimed at maximizing the cost function. By virtue of the quadratic technique, the optimization problem can be solved by dividing into two subproblems, i.e., computing the weight for each relative motion according to the current residuals and solving a second-order cone program problem (SOCP) for the increment in the next iteration. We also provide a novel strategy for determining the kernel width which ensures that our method can efficiently exploit information redundancy supplied by relative motions in the presence of many outliers. Finally, we compare the proposed method with other MA-based multi-view registration methods to verify its performance. Experimental tests on synthetic and real data demonstrate that our method achieves superior performance in terms of efficiency, accuracy and robustness.

Zhu Cheng, Zhan Wang, Haitao Liu et al.

Tuning stepsize between convergence rate and steady state error level or stability is a problem in some subspace tracking schemes. Methods in DPM and OJA class may show sparks in their steady state error sometimes, even with a rather small stepsize. By a study on the schemes' updating formula, it is found that the update only happens in a specific plane but not all the subspace basis. Through an analysis on relationship between the vectors in that plane, an amendment as needed is made on the algorithm routine to fix the problem by constricting the stepsize at every update step. The simulation confirms elimination of the sparks.

Huifa Li, Jie Fu, Zhili Chen et al.

Single-cell RNA sequencing (scRNA-seq) is important to transcriptomic analysis of gene expression. Recently, deep learning has facilitated the analysis of high-dimensional single-cell data. Unfortunately, deep learning models may leak sensitive information about users. As a result, Differential Privacy (DP) is increasingly used to protect privacy. However, existing DP methods usually perturb whole neural networks to achieve differential privacy, and hence result in great performance overheads. To address this challenge, in this paper, we take advantage of the uniqueness of the autoencoder that it outputs only the dimension-reduced vector in the middle of the network, and design a Differentially Private Deep Contrastive Autoencoder Network (DP-DCAN) by partial network perturbation for single-cell clustering. Since only partial network is added with noise, the performance improvement is obvious and twofold: one part of network is trained with less noise due to a bigger privacy budget, and the other part is trained without any noise. Experimental results of six datasets have verified that DP-DCAN is superior to the traditional DP scheme with whole network perturbation. Moreover, DP-DCAN demonstrates strong robustness to adversarial attacks.

Zhendong Guo, Yew-Soon Ong, Tiantian He et al.

Bayesian optimization (BO) is well known to be sample-efficient for solving black-box problems. However, the BO algorithms can sometimes get stuck in suboptimal solutions even with plenty of samples. Intrinsically, such suboptimal problem of BO can attribute to the poor surrogate accuracy of the trained Gaussian process (GP), particularly that in the regions where the optimal solutions locate. Hence, we propose to build multiple GP models instead of a single GP surrogate to complement each other and thus resolving the suboptimal problem of BO. Nevertheless, according to the bias-variance tradeoff equation, the individual prediction errors can increase when increasing the diversity of models, which may lead to even worse overall surrogate accuracy. On the other hand, based on the theory of Rademacher complexity, it has been proved that exploiting the agreement of models on unlabeled information can help to reduce the complexity of the hypothesis space, and therefore achieving the required surrogate accuracy with fewer samples. Such value of model agreement has been extensively demonstrated for co-training style algorithms to boost model accuracy with a small portion of samples. Inspired by the above, we propose a novel BO algorithm labeled as co-learning BO (CLBO), which exploits both model diversity and agreement on unlabeled information to improve the overall surrogate accuracy with limited samples, and therefore achieving more efficient global optimization. Through tests on five numerical toy problems and three engineering benchmarks, the effectiveness of proposed CLBO has been well demonstrated.

Haitao Liu, Kai Wu, Yew-Soon Ong et al.

Multi-task Gaussian process (MTGP) is a well-known non-parametric Bayesian model for learning correlated tasks effectively by transferring knowledge across tasks. But current MTGPs are usually limited to the multi-task scenario defined in the same input domain, leaving no space for tackling the heterogeneous case, i.e., the features of input domains vary over tasks. To this end, this paper presents a novel heterogeneous stochastic variational linear model of coregionalization (HSVLMC) model for simultaneously learning the tasks with varied input domains. Particularly, we develop the stochastic variational framework with Bayesian calibration that (i) takes into account the effect of dimensionality reduction raised by domain mappings in order to achieve effective input alignment; and (ii) employs a residual modeling strategy to leverage the inductive bias brought by prior domain mappings for better model inference. Finally, the superiority of the proposed model against existing LMC models has been extensively verified on diverse heterogeneous multi-task cases and a practical multi-fidelity steam turbine exhaust problem.

Haitao Liu, Jiaqi Ding, Xinyu Xie et al.

Multi-task regression attempts to exploit the task similarity in order to achieve knowledge transfer across related tasks for performance improvement. The application of Gaussian process (GP) in this scenario yields the non-parametric yet informative Bayesian multi-task regression paradigm. Multi-task GP (MTGP) provides not only the prediction mean but also the associated prediction variance to quantify uncertainty, thus gaining popularity in various scenarios. The linear model of coregionalization (LMC) is a well-known MTGP paradigm which exploits the dependency of tasks through linear combination of several independent and diverse GPs. The LMC however suffers from high model complexity and limited model capability when handling complicated multi-task cases. To this end, we develop the neural embedding of coregionalization that transforms the latent GPs into a high-dimensional latent space to induce rich yet diverse behaviors. Furthermore, we use advanced variational inference as well as sparse approximation to devise a tight and compact evidence lower bound (ELBO) for higher quality of scalable model inference. Extensive numerical experiments have been conducted to verify the higher prediction quality and better generalization of our model, named NSVLMC, on various real-world multi-task datasets and the cross-fluid modeling of unsteady fluidized bed.

Haitao Liu, Changjun Liu, Xiaomo Jiang et al.

The demand of probabilistic time series forecasting has been recently raised in various dynamic system scenarios, for example, system identification and prognostic and health management of machines. To this end, we combine the advances in both deep generative models and state space model (SSM) to come up with a novel, data-driven deep probabilistic sequence model. Specifically, we follow the popular encoder-decoder generative structure to build the recurrent neural networks (RNN) assisted variational sequence model on an augmented recurrent input space, which could induce rich stochastic sequence dependency. Besides, in order to alleviate the inconsistency issue of the posterior between training and predicting as well as improving the mining of dynamic patterns, we (i) propose using a lagged hybrid output as input for the posterior at next time step, which brings training and predicting into alignment; and (ii) further devise a generalized auto-regressive strategy that encodes all the historical dependencies for the posterior. Thereafter, we first investigate the methodological characteristics of the proposed deep probabilistic sequence model on toy cases, and then comprehensively demonstrate the superiority of our model against existing deep probabilistic SSM models through extensive numerical experiments on eight system identification benchmarks from various dynamic systems. Finally, we apply our sequence model to a real-world centrifugal compressor forecasting problem, and again verify its outstanding performance by quantifying the time series predictive distribution.

Shuiyuan Yu, Chunshan Xu, Haitao Liu

Traditional linguistic theories have largely regard language as a formal system composed of rigid rules. However, their failures in processing real language, the recent successes in statistical natural language processing, and the findings of many psychological experiments have suggested that language may be more a probabilistic system than a formal system, and thus cannot be faithfully modeled with the either/or rules of formal linguistic theory. The present study, based on authentic language data, confirmed that those important linguistic issues, such as linguistic universal, diachronic drift, and language variations can be translated into probability and frequency patterns in parole. These findings suggest that human language may well be probabilistic systems by nature, and that statistical may well make inherent properties of human languages.

Haitao Liu, Yew-Soon Ong, Xiaomo Jiang et al.

For a learning task, Gaussian process (GP) is interested in learning the statistical relationship between inputs and outputs, since it offers not only the prediction mean but also the associated variability. The vanilla GP however struggles to learn complicated distribution with the property of, e.g., heteroscedastic noise, multi-modality and non-stationarity, from massive data due to the Gaussian marginal and the cubic complexity. To this end, this article studies new scalable GP paradigms including the non-stationary heteroscedastic GP, the mixture of GPs and the latent GP, which introduce additional latent variables to modulate the outputs or inputs in order to learn richer, non-Gaussian statistical representation. We further resort to different variational inference strategies to arrive at analytical or tighter evidence lower bounds (ELBOs) of the marginal likelihood for efficient and effective model training. Extensive numerical experiments against state-of-the-art GP and neural network (NN) counterparts on various tasks verify the superiority of these scalable modulated GPs, especially the scalable latent GP, for learning diverse data distributions.

Haitao Liu, Yew-Soon Ong, Xiaomo Jiang et al.

Deep kernel learning (DKL) leverages the connection between Gaussian process (GP) and neural networks (NN) to build an end-to-end, hybrid model. It combines the capability of NN to learn rich representations under massive data and the non-parametric property of GP to achieve automatic regularization that incorporates a trade-off between model fit and model complexity. However, the deterministic encoder may weaken the model regularization of the following GP part, especially on small datasets, due to the free latent representation. We therefore present a complete deep latent-variable kernel learning (DLVKL) model wherein the latent variables perform stochastic encoding for regularized representation. We further enhance the DLVKL from two aspects: (i) the expressive variational posterior through neural stochastic differential equation (NSDE) to improve the approximation quality, and (ii) the hybrid prior taking knowledge from both the SDE prior and the posterior to arrive at a flexible trade-off. Intensive experiments imply that the DLVKL-NSDE performs similarly to the well calibrated GP on small datasets, and outperforms existing deep GPs on large datasets.

Haitao Liu, Yew-Soon Ong, Ziwei Yu et al.

Gaussian process classification (GPC) provides a flexible and powerful statistical framework describing joint distributions over function space. Conventional GPCs however suffer from (i) poor scalability for big data due to the full kernel matrix, and (ii) intractable inference due to the non-Gaussian likelihoods. Hence, various scalable GPCs have been proposed through (i) the sparse approximation built upon a small inducing set to reduce the time complexity; and (ii) the approximate inference to derive analytical evidence lower bound (ELBO). However, these scalable GPCs equipped with analytical ELBO are limited to specific likelihoods or additional assumptions. In this work, we present a unifying framework which accommodates scalable GPCs using various likelihoods. Analogous to GP regression (GPR), we introduce additive noises to augment the probability space for (i) the GPCs with step, (multinomial) probit and logit likelihoods via the internal variables; and particularly, (ii) the GPC using softmax likelihood via the noise variables themselves. This leads to unified scalable GPCs with analytical ELBO by using variational inference. Empirically, our GPCs showcase better results than state-of-the-art scalable GPCs for extensive binary/multi-class classification tasks with up to two million data points.

Haitao Liu, Randy C. Paffenroth, Jian Zou et al.

Anomalies and outliers are common in real-world data, and they can arise from many sources, such as sensor faults. Accordingly, anomaly detection is important both for analyzing the anomalies themselves and for cleaning the data for further analysis of its ambient structure. Nonetheless, a precise definition of anomalies is important for automated detection and herein we approach such problems from the perspective of detecting sparse latent effects embedded in large collections of noisy data. Standard Graphical Lasso-based techniques can identify the conditional dependency structure of a collection of random variables based on their sample covariance matrix. However, classic Graphical Lasso is sensitive to outliers in the sample covariance matrix. In particular, several outliers in a sample covariance matrix can destroy the sparsity of its inverse. Accordingly, we propose a novel optimization problem that is similar in spirit to Robust Principal Component Analysis (RPCA) and splits the sample covariance matrix $M$ into two parts, $M=F+S$, where $F$ is the cleaned sample covariance whose inverse is sparse and computable by Graphical Lasso, and $S$ contains the outliers in $M$. We accomplish this decomposition by adding an additional $ \ell_1$ penalty to classic Graphical Lasso, and name it "Robust Graphical Lasso (Rglasso)". Moreover, we propose an Alternating Direction Method of Multipliers (ADMM) solution to the optimization problem which scales to large numbers of unknowns. We evaluate our algorithm on both real and synthetic datasets, obtaining interpretable results and outperforming the standard robust Minimum Covariance Determinant (MCD) method and Robust Principal Component Analysis (RPCA) regarding both accuracy and speed.

Haitao Liu, Yew-Soon Ong, Jianfei Cai

Heteroscedastic regression considering the varying noises among observations has many applications in the fields like machine learning and statistics. Here we focus on the heteroscedastic Gaussian process (HGP) regression which integrates the latent function and the noise function together in a unified non-parametric Bayesian framework. Though showing remarkable performance, HGP suffers from the cubic time complexity, which strictly limits its application to big data. To improve the scalability, we first develop a variational sparse inference algorithm, named VSHGP, to handle large-scale datasets. Furthermore, two variants are developed to improve the scalability and capability of VSHGP. The first is stochastic VSHGP (SVSHGP) which derives a factorized evidence lower bound, thus enhancing efficient stochastic variational inference. The second is distributed VSHGP (DVSHGP) which (i) follows the Bayesian committee machine formalism to distribute computations over multiple local VSHGP experts with many inducing points; and (ii) adopts hybrid parameters for experts to guard against over-fitting and capture local variety. The superiority of DVSHGP and SVSHGP as compared to existing scalable heteroscedastic/homoscedastic GPs is then extensively verified on various datasets.

Haitao Liu, Jianfei Cai, Yew-Soon Ong et al.

As a non-parametric Bayesian model which produces informative predictive distribution, Gaussian process (GP) has been widely used in various fields, like regression, classification and optimization. The cubic complexity of standard GP however leads to poor scalability, which poses challenges in the era of big data. Hence, various scalable GPs have been developed in the literature in order to improve the scalability while retaining desirable prediction accuracy. This paper devotes to investigating the methodological characteristics and performance of representative global and local scalable GPs including sparse approximations and local aggregations from four main perspectives: scalability, capability, controllability and robustness. The numerical experiments on two toy examples and five real-world datasets with up to 250K points offer the following findings. In terms of scalability, most of the scalable GPs own a time complexity that is linear to the training size. In terms of capability, the sparse approximations capture the long-term spatial correlations, the local aggregations capture the local patterns but suffer from over-fitting in some scenarios. In terms of controllability, we could improve the performance of sparse approximations by simply increasing the inducing size. But this is not the case for local aggregations. In terms of robustness, local aggregations are robust to various initializations of hyperparameters due to the local attention mechanism. Finally, we highlight that the proper hybrid of global and local scalable GPs may be a promising way to improve both the model capability and scalability for big data.

Shuiyuan Yu, Chunshan Xu, Haitao Liu

Zipf's law has been found in many human-related fields, including language, where the frequency of a word is persistently found as a power law function of its frequency rank, known as Zipf's law. However, there is much dispute whether it is a universal law or a statistical artifact, and little is known about what mechanisms may have shaped it. To answer these questions, this study conducted a large scale cross language investigation into Zipf's law. The statistical results show that Zipf's laws in 50 languages all share a 3-segment structural pattern, with each segment demonstrating distinctive linguistic properties and the lower segment invariably bending downwards to deviate from theoretical expectation. This finding indicates that this deviation is a fundamental and universal feature of word frequency distributions in natural languages, not the statistical error of low frequency words. A computer simulation based on the dual-process theory yields Zipf's law with the same structural pattern, suggesting that Zipf's law of natural languages are motivated by common cognitive mechanisms. These results show that Zipf's law in languages is motivated by cognitive mechanisms like dual-processing that govern human verbal behaviors.

Haitao Liu, Yew-Soon Ong, Xiaobo Shen et al.

The vast quantity of information brought by big data as well as the evolving computer hardware encourages success stories in the machine learning community. In the meanwhile, it poses challenges for the Gaussian process (GP) regression, a well-known non-parametric and interpretable Bayesian model, which suffers from cubic complexity to data size. To improve the scalability while retaining desirable prediction quality, a variety of scalable GPs have been presented. But they have not yet been comprehensively reviewed and analyzed in order to be well understood by both academia and industry. The review of scalable GPs in the GP community is timely and important due to the explosion of data size. To this end, this paper is devoted to the review on state-of-the-art scalable GPs involving two main categories: global approximations which distillate the entire data and local approximations which divide the data for subspace learning. Particularly, for global approximations, we mainly focus on sparse approximations comprising prior approximations which modify the prior but perform exact inference, posterior approximations which retain exact prior but perform approximate inference, and structured sparse approximations which exploit specific structures in kernel matrix; for local approximations, we highlight the mixture/product of experts that conducts model averaging from multiple local experts to boost predictions. To present a complete review, recent advances for improving the scalability and capability of scalable GPs are reviewed. Finally, the extensions and open issues regarding the implementation of scalable GPs in various scenarios are reviewed and discussed to inspire novel ideas for future research avenues.

Haitao Liu, Jianfei Cai, Yi Wang et al.

In order to scale standard Gaussian process (GP) regression to large-scale datasets, aggregation models employ factorized training process and then combine predictions from distributed experts. The state-of-the-art aggregation models, however, either provide inconsistent predictions or require time-consuming aggregation process. We first prove the inconsistency of typical aggregations using disjoint or random data partition, and then present a consistent yet efficient aggregation model for large-scale GP. The proposed model inherits the advantages of aggregations, e.g., closed-form inference and aggregation, parallelization and distributed computing. Furthermore, theoretical and empirical analyses reveal that the new aggregation model performs better due to the consistent predictions that converge to the true underlying function when the training size approaches infinity.

Shuiyuan Yu, Jin Cong, Junying Liang et al.

Sentence is a basic linguistic unit, however, little is known about how information content is distributed across different positions of a sentence. Based on authentic language data of English, the present study calculated the entropy and other entropy-related statistics for different sentence positions. The statistics indicate a three-step staircase-shaped distribution pattern, with entropy in the initial position lower than the medial positions (positions other than the initial and final), the medial positions lower than the final position and the medial positions showing no significant difference. The results suggest that: (1) the hypotheses of Constant Entropy Rate and Uniform Information Density do not hold for the sentence-medial positions; (2) the context of a word in a sentence should not be simply defined as all the words preceding it in the same sentence; and (3) the contextual information content in a sentence does not accumulate incrementally but follows a pattern of "the whole is greater than the sum of parts".

Shuiyuan Yu, Junying Liang, Haitao Liu

The power law is ubiquitous in natural and social phenomena, and is considered as a universal relationship between the frequency and its rank for diverse social systems. However, a general model is still lacking to interpret why these seemingly unrelated systems share great similarity. Through a detailed analysis of natural language texts and simulation experiments based on the proposed 'Hierarchical Selection Model', we found that the existence of hierarchies and human's pursuit of top hierarchy lead to the power law. Further, the power law is a statistical and emergent performance of hierarchies, and it is the universality of hierarchies that contributes to the ubiquity of the power law.

Haitao Liu, Chunshan Xu, Junying Liang

In the recent issue of PNAS, Futrell et al. claims that their study of 37 languages gives the first large scale cross-language evidence for Dependency Length Minimization, which is an overstatement that ignores similar previous researches. In addition,this study seems to pay no attention to factors like the uniformity of genres,which weakens the validity of the argument that DLM is universal. Another problem is that this study sets the baseline random language as projective, which fails to truly uncover the difference between natural language and random language, since projectivity is an important feature of many natural languages. Finally, the paper contends an "apparent relationship between head finality and dependency length" despite the lack of an explicit statistical comparison, which renders this conclusion rather hasty and improper.

Qian Lu, Chunshan Xu, Haitao Liu

This paper hypothesizes that chunking plays important role in reducing dependency distance and dependency crossings. Computer simulations, when compared with natural languages,show that chunking reduces mean dependency distance (MDD) of a linear sequence of nodes (constrained by continuity or projectivity) to that of natural languages. More interestingly, chunking alone brings about less dependency crossings as well, though having failed to reduce them, to such rarity as found in human languages. These results suggest that chunking may play a vital role in the minimization of dependency distance, and a somewhat contributing role in the rarity of dependency crossing. In addition, the results point to a possibility that the rarity of dependency crossings is not a mere side-effect of minimization of dependency distance, but a linguistic phenomenon with its own motivations.

Ramon Ferrer-i-Cancho, Haitao Liu

Mixing dependency lengths from sequences of different length is a common practice in language research. However, the empirical distribution of dependency lengths of sentences of the same length differs from that of sentences of varying length and the distribution of dependency lengths depends on sentence length for real sentences and also under the null hypothesis that dependencies connect vertices located in random positions of the sequence. This suggests that certain results, such as the distribution of syntactic dependency lengths mixing dependencies from sentences of varying length, could be a mere consequence of that mixing. Furthermore, differences in the global averages of dependency length (mixing lengths from sentences of varying length) for two different languages do not simply imply a priori that one language optimizes dependency lengths better than the other because those differences could be due to differences in the distribution of sentence lengths and other factors.