Package for Fast ABC-Boost

This report presents the open-source package which implements the series of our boosting works in the past years. In particular, the package includes mainly three lines of techniques, among which the following two are already the standard implementations in popular boosted tree platforms: (i) The histogram-based (feature-binning) approach makes the tree implementation convenient and efficient. In Li et al (2007), a simple fixed-length adaptive binning algorithm was developed. In this report, we demonstrate that such a simple algorithm is still surprisingly effective compared to more sophisticated variants in popular tree platforms. (ii) The explicit gain formula in Li (20010) for tree splitting based on second-order derivatives of the loss function typically improves, often considerably, over the first-order methods. Although the gain formula in Li (2010) was derived for logistic regression loss, it is a generic formula for loss functions with second-derivatives. For example, the open-source package also includes $L_p$ regression for $p\geq 1$. The main contribution of this package is the ABC-Boost (adaptive base class boosting) for multi-class classification. The initial work in Li (2008) derived a new set of derivatives of the classical multi-class logistic regression by specifying a "base class". The accuracy can be substantially improved if the base class is chosen properly. The major technical challenge is to design a search strategy to select the base class. The prior published works implemented an exhaustive search procedure to find the base class which is computationally too expensive. Recently, a new report (Li and Zhao, 20022) presents a unified framework of "Fast ABC-Boost" which allows users to efficiently choose the proper search space for the base class. The package provides interfaces for linux, windows, mac, matlab, R, python.

pGMM Kernel Regression and Comparisons with Boosted Trees

In this work, we demonstrate the advantage of the pGMM (``powered generalized min-max'') kernel in the context of (ridge) regression. In recent prior studies, the pGMM kernel has been extensively evaluated for classification tasks, for logistic regression, support vector machines, as well as deep neural networks. In this paper, we provide an experimental study on ridge regression, to compare the pGMM kernel regression with the ordinary ridge linear regression as well as the RBF kernel ridge regression. Perhaps surprisingly, even without a tuning parameter (i.e., $p=1$ for the power parameter of the pGMM kernel), the pGMM kernel already performs well. Furthermore, by tuning the parameter $p$, this (deceptively simple) pGMM kernel even performs quite comparably to boosted trees. Boosting and boosted trees are very popular in machine learning practice. For regression tasks, typically, practitioners use $L_2$ boost, i.e., for minimizing the $L_2$ loss. Sometimes for the purpose of robustness, the $L_1$ boost might be a choice. In this study, we implement $L_p$ boost for $p\geq 1$ and include it in the package of ``Fast ABC-Boost''. Perhaps also surprisingly, the best performance (in terms of $L_2$ regression loss) is often attained at $p>2$, in some cases at $p\gg 2$. This phenomenon has already been demonstrated by Li et al (UAI 2010) in the context of k-nearest neighbor classification using $L_p$ distances. In summary, the implementation of $L_p$ boost provides practitioners the additional flexibility of tuning boosting algorithms for potentially achieving better accuracy in regression applications.

Variational Flow Graphical Model

This paper introduces a novel approach to embed flow-based models with hierarchical structures. The proposed framework is named Variational Flow Graphical (VFG) Model. VFGs learn the representation of high dimensional data via a message-passing scheme by integrating flow-based functions through variational inference. By leveraging the expressive power of neural networks, VFGs produce a representation of the data using a lower dimension, thus overcoming the drawbacks of many flow-based models, usually requiring a high dimensional latent space involving many trivial variables. Aggregation nodes are introduced in the VFG models to integrate forward-backward hierarchical information via a message passing scheme. Maximizing the evidence lower bound (ELBO) of data likelihood aligns the forward and backward messages in each aggregation node achieving a consistency node state. Algorithms have been developed to learn model parameters through gradient updating regarding the ELBO objective. The consistency of aggregation nodes enable VFGs to be applicable in tractable inference on graphical structures. Besides representation learning and numerical inference, VFGs provide a new approach for distribution modeling on datasets with graphical latent structures. Additionally, theoretical study shows that VFGs are universal approximators by leveraging the implicitly invertible flow-based structures. With flexible graphical structures and superior excessive power, VFGs could potentially be used to improve probabilistic inference. In the experiments, VFGs achieves improved evidence lower bound (ELBO) and likelihood values on multiple datasets.

Best Subset Selection with Efficient Primal-Dual Algorithm

Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-convex and NP-hard problem. In this paper, we investigate the dual forms of a family of $\ell_0$-regularized problems. An efficient primal-dual method has been developed based on the primal and dual problem structures. By leveraging the dual range estimation along with the incremental strategy, our algorithm potentially reduces redundant computation and improves the solutions of best subset selection. Theoretical analysis and experiments on synthetic and real-world datasets validate the efficiency and statistical properties of the proposed solutions.

$k$-Median Clustering via Metric Embedding: Towards Better Initialization with Differential Privacy

When designing clustering algorithms, the choice of initial centers is crucial for the quality of the learned clusters. In this paper, we develop a new initialization scheme, called HST initialization, for the $k$-median problem in the general metric space (e.g., discrete space induced by graphs), based on the construction of metric embedding tree structure of the data. From the tree, we propose a novel and efficient search algorithm, for good initial centers that can be used subsequently for the local search algorithm. Our proposed HST initialization can produce initial centers achieving lower errors than those from another popular initialization method, $k$-median++, with comparable efficiency. The HST initialization can also be extended to the setting of differential privacy (DP) to generate private initial centers. We show that the error from applying DP local search followed by our private HST initialization improves previous results on the approximation error, and approaches the lower bound within a small factor. Experiments justify the theory and demonstrate the effectiveness of our proposed method. Our approach can also be extended to the $k$-means problem.

Defending Backdoor Attacks on Vision Transformer via Patch Processing

Vision Transformers (ViTs) have a radically different architecture with significantly less inductive bias than Convolutional Neural Networks. Along with the improvement in performance, security and robustness of ViTs are also of great importance to study. In contrast to many recent works that exploit the robustness of ViTs against adversarial examples, this paper investigates a representative causative attack, i.e., backdoor. We first examine the vulnerability of ViTs against various backdoor attacks and find that ViTs are also quite vulnerable to existing attacks. However, we observe that the clean-data accuracy and backdoor attack success rate of ViTs respond distinctively to patch transformations before the positional encoding. Then, based on this finding, we propose an effective method for ViTs to defend both patch-based and blending-based trigger backdoor attacks via patch processing. The performances are evaluated on several benchmark datasets, including CIFAR10, GTSRB, and TinyImageNet, which show the proposed novel defense is very successful in mitigating backdoor attacks for ViTs. To the best of our knowledge, this paper presents the first defensive strategy that utilizes a unique characteristic of ViTs against backdoor attacks.

CGAR: Critic Guided Action Redistribution in Reinforcement Leaning

Training a game-playing reinforcement learning agent requires multiple interactions with the environment. Ignorant random exploration may cause a waste of time and resources. It's essential to alleviate such waste. As discussed in this paper, under the settings of the off-policy actor critic algorithms, we demonstrate that the critic can bring more expected discounted rewards than or at least equal to the actor. Thus, the Q value predicted by the critic is a better signal to redistribute the action originally sampled from the policy distribution predicted by the actor. This paper introduces the novel Critic Guided Action Redistribution (CGAR) algorithm and tests it on the OpenAI MuJoCo tasks. The experimental results demonstrate that our method improves the sample efficiency and achieves state-of-the-art performance. Our code can be found at https://github.com/tairanhuang/CGAR.

Noisy $\ell^{0}$-Sparse Subspace Clustering on Dimensionality Reduced Data

Sparse subspace clustering methods with sparsity induced by $\ell^{0}$-norm, such as $\ell^{0}$-Sparse Subspace Clustering ($\ell^{0}$-SSC)~\citep{YangFJYH16-L0SSC-ijcv}, are demonstrated to be more effective than its $\ell^{1}$ counterpart such as Sparse Subspace Clustering (SSC)~\citep{ElhamifarV13}. However, the theoretical analysis of $\ell^{0}$-SSC is restricted to clean data that lie exactly in subspaces. Real data often suffer from noise and they may lie close to subspaces. In this paper, we show that an optimal solution to the optimization problem of noisy $\ell^{0}$-SSC achieves subspace detection property (SDP), a key element with which data from different subspaces are separated, under deterministic and semi-random model. Our results provide theoretical guarantee on the correctness of noisy $\ell^{0}$-SSC in terms of SDP on noisy data for the first time, which reveals the advantage of noisy $\ell^{0}$-SSC in terms of much less restrictive condition on subspace affinity. In order to improve the efficiency of noisy $\ell^{0}$-SSC, we propose Noisy-DR-$\ell^{0}$-SSC which provably recovers the subspaces on dimensionality reduced data. Noisy-DR-$\ell^{0}$-SSC first projects the data onto a lower dimensional space by random projection, then performs noisy $\ell^{0}$-SSC on the projected data for improved efficiency. Experimental results demonstrate the effectiveness of Noisy-DR-$\ell^{0}$-SSC.

Proximity Graph Maintenance for Fast Online Nearest Neighbor Search

Approximate Nearest Neighbor (ANN) search is a fundamental technique for (e.g.,) the deployment of recommender systems. Recent studies bring proximity graph-based methods into practitioners' attention -- proximity graph-based methods outperform other solutions such as quantization, hashing, and tree-based ANN algorithm families. In current recommendation systems, data point insertions, deletions, and queries are streamed into the system in an online fashion as users and items change dynamically. As proximity graphs are constructed incrementally by inserting data points as new vertices into the graph, online insertions and queries are well-supported in proximity graph. However, a data point deletion incurs removing a vertex from the proximity graph index, while no proper graph index updating mechanisms are discussed in previous studies. To tackle the challenge, we propose an incremental proximity graph maintenance (IPGM) algorithm for online ANN. IPGM supports both vertex deletion and insertion on proximity graphs. Given a vertex deletion request, we thoroughly investigate solutions to update the connections of the vertex. The proposed updating scheme eliminates the performance drop in online ANN methods on proximity graphs, making the algorithm suitable for practical systems.

Planning through Workspace Constraint Satisfaction and Optimization

In this work, we present a workspace-based planning framework, which though using redundant workspace key-points to represent robot states, can take advantage of the interpretable geometric information to derive good quality collision-free paths for even complex robots. Using workspace geometries, we first find collision-free piece-wise linear paths for each key point so that at the endpoints of each segment, the distance constraints are satisfied among the key points. Using these piece-wise linear paths as initial conditions, we can perform optimization steps to quickly find paths that satisfy various constraints and piece together all segments to obtain a valid path. We show that these adjusted paths are unlikely to create a collision, and the proposed approach is fast and can produce good quality results.