arXiv subjects

Xiaofeng Cao

Publications and source records attributed to Xiaofeng Cao.

50 records · Page 3Linked to original sources

arXiv2023

Black-box Generalization of Machine Teaching

Hypothesis-pruning maximizes the hypothesis updates for active learning to find those desired unlabeled data. An inherent assumption is that this learning manner can derive those updates into the optimal hypothesis. However, its convergence may not be guaranteed well if those incremental updates are negative and disordered. In this paper, we introduce a black-box teaching hypothesis $h^\mathcal{T}$ employing a tighter slack term $\left(1+\mathcal{F}^{\mathcal{T}}(\widehat{h}_t)\right)Δ_t$ to replace the typical $2Δ_t$ for pruning. Theoretically, we prove that, under the guidance of this teaching hypothesis, the learner can converge into a tighter generalization error and label complexity bound than those non-educated learners who do not receive any guidance from a teacher:1) the generalization error upper bound can be reduced from $R(h^*)+4Δ_{T-1}$ to approximately $R(h^{\mathcal{T}})+2Δ_{T-1}$, and 2) the label complexity upper bound can be decreased from $4 θ\left(TR(h^{*})+2O(\sqrt{T})\right)$ to approximately $2θ\left(2TR(h^{\mathcal{T}})+3 O(\sqrt{T})\right)$. To be strict with our assumption, self-improvement of teaching is firstly proposed when $h^\mathcal{T}$ loosely approximates $h^*$. Against learning, we further consider two teaching scenarios: teaching a white-box and black-box learner. Experiments verify this idea and show better generalization performance than the fundamental active learning strategies, such as IWAL, IWAL-D, etc.

cs.LG↗

arXiv2023

A Survey of Learning on Small Data: Generalization, Optimization, and Challenge

Learning on big data brings success for artificial intelligence (AI), but the annotation and training costs are expensive. In future, learning on small data that approximates the generalization ability of big data is one of the ultimate purposes of AI, which requires machines to recognize objectives and scenarios relying on small data as humans. A series of learning topics is going on this way such as active learning and few-shot learning. However, there are few theoretical guarantees for their generalization performance. Moreover, most of their settings are passive, that is, the label distribution is explicitly controlled by finite training resources from known distributions. This survey follows the agnostic active sampling theory under a PAC (Probably Approximately Correct) framework to analyze the generalization error and label complexity of learning on small data in model-agnostic supervised and unsupervised fashion. Considering multiple learning communities could produce small data representation and related topics have been well surveyed, we thus subjoin novel geometric representation perspectives for small data: the Euclidean and non-Euclidean (hyperbolic) mean, where the optimization solutions including the Euclidean gradients, non-Euclidean gradients, and Stein gradient are presented and discussed. Later, multiple learning communities that may be improved by learning on small data are summarized, which yield data-efficient representations, such as transfer learning, contrastive learning, graph representation learning. Meanwhile, we find that the meta-learning may provide effective parameter update policies for learning on small data. Then, we explore multiple challenging scenarios for small data, such as the weak supervision and multi-label. Finally, multiple data applications that may benefit from efficient small data representation are surveyed.

cs.LG↗

arXiv2023

Nonparametric Iterative Machine Teaching

In this paper, we consider the problem of Iterative Machine Teaching (IMT), where the teacher provides examples to the learner iteratively such that the learner can achieve fast convergence to a target model. However, existing IMT algorithms are solely based on parameterized families of target models. They mainly focus on convergence in the parameter space, resulting in difficulty when the target models are defined to be functions without dependency on parameters. To address such a limitation, we study a more general task -- Nonparametric Iterative Machine Teaching (NIMT), which aims to teach nonparametric target models to learners in an iterative fashion. Unlike parametric IMT that merely operates in the parameter space, we cast NIMT as a functional optimization problem in the function space. To solve it, we propose both random and greedy functional teaching algorithms. We obtain the iterative teaching dimension (ITD) of the random teaching algorithm under proper assumptions, which serves as a uniform upper bound of ITD in NIMT. Further, the greedy teaching algorithm has a significantly lower ITD, which reaches a tighter upper bound of ITD in NIMT. Finally, we verify the correctness of our theoretical findings with extensive experiments in nonparametric scenarios.

cs.LG↗

arXiv2023

Hyperbolic Uncertainty Aware Semantic Segmentation

Semantic segmentation (SS) aims to classify each pixel into one of the pre-defined classes. This task plays an important role in self-driving cars and autonomous drones. In SS, many works have shown that most misclassified pixels are commonly near object boundaries with high uncertainties. However, existing SS loss functions are not tailored to handle these uncertain pixels during training, as these pixels are usually treated equally as confidently classified pixels and cannot be embedded with arbitrary low distortion in Euclidean space, thereby degenerating the performance of SS. To overcome this problem, this paper designs a "Hyperbolic Uncertainty Loss" (HyperUL), which dynamically highlights the misclassified and high-uncertainty pixels in Hyperbolic space during training via the hyperbolic distances. The proposed HyperUL is model agnostic and can be easily applied to various neural architectures. After employing HyperUL to three recent SS models, the experimental results on Cityscapes and UAVid datasets reveal that the segmentation performance of existing SS models can be consistently improved.

cs.CV↗

arXiv2022

One-shot Machine Teaching: Cost Very Few Examples to Converge Faster

Artificial intelligence is to teach machines to take actions like humans. To achieve intelligent teaching, the machine learning community becomes to think about a promising topic named machine teaching where the teacher is to design the optimal (usually minimal) teaching set given a target model and a specific learner. However, previous works usually require numerous teaching examples along with large iterations to guide learners to converge, which is costly. In this paper, we consider a more intelligent teaching paradigm named one-shot machine teaching which costs fewer examples to converge faster. Different from typical teaching, this advanced paradigm establishes a tractable mapping from the teaching set to the model parameter. Theoretically, we prove that this mapping is surjective, which serves to an existence guarantee of the optimal teaching set. Then, relying on the surjective mapping from the teaching set to the parameter, we develop a design strategy of the optimal teaching set under appropriate settings, of which two popular efficiency metrics, teaching dimension and iterative teaching dimension are one. Extensive experiments verify the efficiency of our strategy and further demonstrate the intelligence of this new teaching paradigm.

cs.LG↗

arXiv2022

Data-Efficient Learning via Minimizing Hyperspherical Energy

Deep learning on large-scale data is dominant nowadays. The unprecedented scale of data has been arguably one of the most important driving forces for the success of deep learning. However, there still exist scenarios where collecting data or labels could be extremely expensive, e.g., medical imaging and robotics. To fill up this gap, this paper considers the problem of data-efficient learning from scratch using a small amount of representative data. First, we characterize this problem by active learning on homeomorphic tubes of spherical manifolds. This naturally generates feasible hypothesis class. With homologous topological properties, we identify an important connection -- finding tube manifolds is equivalent to minimizing hyperspherical energy (MHE) in physical geometry. Inspired by this connection, we propose a MHE-based active learning (MHEAL) algorithm, and provide comprehensive theoretical guarantees for MHEAL, covering convergence and generalization analysis. Finally, we demonstrate the empirical performance of MHEAL in a wide range of applications on data-efficient learning, including deep clustering, distribution matching, version space sampling and deep active learning.

cs.LG↗

arXiv2021

Bayesian Active Learning by Disagreements: A Geometric Perspective

We present geometric Bayesian active learning by disagreements (GBALD), a framework that performs BALD on its core-set construction interacting with model uncertainty estimation. Technically, GBALD constructs core-set on ellipsoid, not typical sphere, preventing low-representative elements from spherical boundaries. The improvements are twofold: 1) relieve uninformative prior and 2) reduce redundant estimations. Theoretically, geodesic search with ellipsoid can derive tighter lower bound on error and easier to achieve zero error than with sphere. Experiments show that GBALD has slight perturbations to noisy and repeated samples, and outperforms BALD, BatchBALD and other existing deep active learning approaches.

cs.LG↗

arXiv2021

Distribution Matching for Machine Teaching

Machine teaching is an inverse problem of machine learning that aims at steering the student learner towards its target hypothesis, in which the teacher has already known the student's learning parameters. Previous studies on machine teaching focused on balancing the teaching risk and cost to find those best teaching examples deriving the student model. This optimization solver is in general ineffective when the student learner does not disclose any cue of the learning parameters. To supervise such a teaching scenario, this paper presents a distribution matching-based machine teaching strategy. Specifically, this strategy backwardly and iteratively performs the halving operation on the teaching cost to find a desired teaching set. Technically, our strategy can be expressed as a cost-controlled optimization process that finds the optimal teaching examples without further exploring in the parameter distribution of the student learner. Then, given any a limited teaching cost, the training examples will be closed-form. Theoretical analysis and experiment results demonstrate this strategy.

cs.LG↗

arXiv2020

A Divide-and-Conquer Approach to Geometric Sampling for Active Learning

Active learning (AL) repeatedly trains the classifier with the minimum labeling budget to improve the current classification model. The training process is usually supervised by an uncertainty evaluation strategy. However, the uncertainty evaluation always suffers from performance degeneration when the initial labeled set has insufficient labels. To completely eliminate the dependence on the uncertainty evaluation sampling in AL, this paper proposes a divide-and-conquer idea that directly transfers the AL sampling as the geometric sampling over the clusters. By dividing the points of the clusters into cluster boundary and core points, we theoretically discuss their margin distance and {hypothesis relationship}. With the advantages of cluster boundary points in the above two properties, we propose a Geometric Active Learning (GAL) algorithm by knight's tour. Experimental studies of the two reported experimental tasks including cluster boundary detection and AL classification show that the proposed GAL method significantly outperforms the state-of-the-art baselines.

cs.LG↗

arXiv2020

A Structured Perspective of Volumes on Active Learning

Active Learning (AL) is a learning task that requires learners interactively query the labels of the sampled unlabeled instances to minimize the training outputs with human supervisions. In theoretical study, learners approximate the version space which covers all possible classification hypothesis into a bounded convex body and try to shrink the volume of it into a half-space by a given cut size. However, only the hypersphere with finite VC dimensions has obtained formal approximation guarantees that hold when the classes of Euclidean space are separable with a margin. In this paper, we approximate the version space to a structured {hypersphere} that covers most of the hypotheses, and then divide the available AL sampling approaches into two kinds of strategies: Outer Volume Sampling and Inner Volume Sampling. After providing provable guarantees for the performance of AL in version space, we aggregate the two kinds of volumes to eliminate their sampling biases via finding the optimal inscribed hyperspheres in the enclosing space of outer volume. To touch the version space from Euclidean space, we propose a theoretical bridge called Volume-based Model that increases the `sampling target-independent'. In non-linear feature space, spanned by kernel, we use sequential optimization to globally optimize the original space to a sparse space by halving the size of the kernel space. Then, the EM (Expectation Maximization) model which returns the local center helps us to find a local representation. To describe this process, we propose an easy-to-implement algorithm called Volume-based AL (VAL).

cs.LG↗

arXiv2020

Target-Independent Active Learning via Distribution-Splitting

To reduce the label complexity in Agnostic Active Learning (A^2 algorithm), volume-splitting splits the hypothesis edges to reduce the Vapnik-Chervonenkis (VC) dimension in version space. However, the effectiveness of volume-splitting critically depends on the initial hypothesis and this problem is also known as target-dependent label complexity gap. This paper attempts to minimize this gap by introducing a novel notion of number density which provides a more natural and direct way to describe the hypothesis distribution than volume. By discovering the connections between hypothesis and input distribution, we map the volume of version space into the number density and propose a target-independent distribution-splitting strategy with the following advantages: 1) provide theoretical guarantees on reducing label complexity and error rate as volume-splitting; 2) break the curse of initial hypothesis; 3) provide model guidance for a target-independent AL algorithm in real AL tasks. With these guarantees, for AL application, we then split the input distribution into more near-optimal spheres and develop an application algorithm called Distribution-based A^2 (DA^2). Experiments further verify the effectiveness of the halving and querying abilities of DA^2. Contributions of this paper are as follows.

cs.LG↗

arXiv2020

Edge Federation: Towards an Integrated Service Provisioning Model

Edge computing is a promising computing paradigm for pushing the cloud service to the network edge. To this end, edge infrastructure providers (EIPs) need to bring computation and storage resources to the network edge and allow edge service providers (ESPs) to provision latency-critical services to users. Currently, EIPs prefer to establish a series of private edge-computing environments to serve specific requirements of users. This kind of resource provisioning mechanism severely limits the development and spread of edge computing for serving diverse user requirements. To this end, we propose an integrated resource provisioning model, named edge federation, to seamlessly realize the resource cooperation and service provisioning across standalone edge computing providers and clouds. To efficiently schedule and utilize the resources across multiple EIPs, we systematically characterize the provisioning process as a large-scale linear programming (LP) problem and transform it into an easily solved form. Accordingly, we design a dynamic algorithm to tackle the varying service demands from users. We conduct extensive experiments over the base station networks in Toronto city. Compared with the existing fixed contract model and multihoming model, edge federation can reduce the overall cost of EIPs by 23.3% to 24.5%, and 15.5% to 16.3%, respectively.

cs.NI↗

arXiv2019

Learning Image-Specific Attributes by Hyperbolic Neighborhood Graph Propagation

As a kind of semantic representation of visual object descriptions, attributes are widely used in various computer vision tasks. In most of existing attribute-based research, class-specific attributes (CSA), which are class-level annotations, are usually adopted due to its low annotation cost for each class instead of each individual image. However, class-specific attributes are usually noisy because of annotation errors and diversity of individual images. Therefore, it is desirable to obtain image-specific attributes (ISA), which are image-level annotations, from the original class-specific attributes. In this paper, we propose to learn image-specific attributes by graph-based attribute propagation. Considering the intrinsic property of hyperbolic geometry that its distance expands exponentially, hyperbolic neighborhood graph (HNG) is constructed to characterize the relationship between samples. Based on HNG, we define neighborhood consistency for each sample to identify inconsistent samples. Subsequently, inconsistent samples are refined based on their neighbors in HNG. Extensive experiments on five benchmark datasets demonstrate the significant superiority of the learned image-specific attributes over the original class-specific attributes in the zero-shot object classification task.

cs.CV↗

arXiv2008

Frequency Variation of the Kilohertz Quasi-periodic Oscillations and the Flux of the Band-limited Noise in Scorpius X-1

We study the kilohertz quasi-periodic oscillations (kHz QPOs) and the band-limited noise (BLN) in the 0.5--16 Hz range observed simultaneously on the horizontal branch (HB) and on the upper normal branch (NB) of the brightest neutron star Low-mass X-ray Binary (LMXB) Scorpius X--1 with the observations performed with the {\it Rossi X-Ray Timing Explorer (RXTE)}. We find that the twin kHz QPO frequencies are positively correlated with the flux variations taking place on the BLN time scales on the HB, in contrast to the anti-correlation held on the time scale of the normal branch oscillation (NBO) on the NB reported previously, suggesting that although they occur in sequence along the color-color tracks, the BLN and the NBO are of different origins. We also show the evidence that the frequency separation between the twin kHz QPOs decreases with the flux by $2\sim~3$ Hz on the BLN time scales, which is consistent with the trend on the longer time scale that the Z source traces the HB. This further suggests that the flux variation associated with the BLN originates from the mass accretion rate variation in the disk accretion flow. We discuss the implications of these results for our understanding of the BLN.

astro-ph↗