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In a Data-Generating Experiment, the observed sample, x, has intractable or unavailable c.d.f., F_θ, and θ’s statistical nature is unknown; θ is element of metric space (Θ, dΘ). Matching estimates of θ are introduced, learning from the “best” x-matches with samples X^∗ from F_{θ^∗}, θ^∗ ∈ Θ. Under mild conditions, these nonparametric estimates are uniformly consistent and the upper bounds on their rates of convergence in probability have the same rate and depend on the Kolmogorov entropies of an increasing sequence of sets covering Θ. When Θ ⊆ Rm and the observations are i.i.d. the upper bounds can be, \sqrt{log n}/\sqrt{n} when m is known, and \sqrt{m_n·log n}/\sqrt{n} when m is unknown; m ≥ 1, m_n ↑ ∞ at a desired rate. Upper bounds can also be obtained for dependent observations. These rates hold for observations in R^d, complementing recent results obtained for real, i.i.d. observations, under stronger assumptions and using weak probability distances; d ≥ 1. In simulations, the Matching estimates are successful for the mixture of 2 normals and for Tukey’s (a, b, g, h) and the (a, b, g, k) models. Computers’ evolution will allow for more and faster comparisons, resulting in improved Matching estimates for universal use in Machine Learning.

When sample, X = x, is observed from intractable c.d.f. Fθ, or a Black-Box with input θ, an Approximate Bayesian Computation (ABC) method provides approximate posterior, π_ϵ. θ^∗ is included in the support of π_ϵ when the Matching distance ρ(S(x^∗), S(x)) ≤ ϵ; x^∗ is a sample drawn from F_{θ^∗}, θ^∗ is obtained from prior π, S is a summary statistic, ϵ > 0. ABC concerns include: the use of only one sample, x^∗, for each θ^∗; the choices of S, ρ and ϵ; π_ϵ(θ^∗), which is determined by arbitrary kernel, K(x, x^∗; ϵ), creating visual π_ϵ-artifacts. The concerns are accommodated with the introduced Fiducial(F)-ABC for all (θ^∗ drawn): M x^∗ are drawn from F_{θ^∗}; a universal S is used, the empirical measure indexed by sets which activate its sufficiency for exchangeable observations-vectors and have been neglected; a strong, probability distance ρ is used, inherently connected with S and Matching; light is thrown to ϵ’s nature and value; πϵ is obtained from the proportions of x∗ matching x. F-ABC for all posterior is closer to Bayesian philosophy, which does not use θ^∗-exclusions. Under few, mild assumptions, π_ϵ converges to the posterior, π(θ|x), when ϵ ↓ 0, and rates of concentration of T (F_{θ^∗}) to T (F_θ) are obtained when n ↑ ∞; T is a functional. Satisfactory F-ABC for all θ^∗ drawn posteriors are depicted for parametric and data generating models, including Tukey’s (a, b, g, h)-model, a 5-parameter normal mixture and a time series model. Various advantages of the F-ABC for all are presented over coarsened posteriors for observations in R^d, d ≥ 1.

In a Data-Generating Experiment (DGE), the data, X, is often obtained either from a Black-Box with inputs θ and Y, or from a Quantile function or a learning machine, f(Y, θ); θ is unknown, element of metric space (Θ, ρ), Y is random. If X has intractable or unknown c.d.f., Fθ, non-identifiability of θ cannot be confirmed and when present, among others, limits the predictive accuracy of the learned model, f(Y, \hat{θ}); \hat{θ} estimate of θ. In Machine Learning, non-identifiability of θ is ubiquitous and its extent is a criterion for selecting a learning machine. Empirical indices, EDI and PPVI, are introduced using P-values of Kolmogorov-Smirnov tests: i) to confirm almost surely, using generated data, the discrimination of θ from θ^∗, namely that the Kolmogorov distance, dK(Fθ, Fθ^∗), is positive, ii) to confirm identifiability of θ(∈ Θ) by repeating i) for θ^∗ in a sieve of Θ, since neighboring parameter values are in practice indistinguishable, and iii) most important, to compare EDI-graphs of DGEs, preferring more discrimination and less non-identifiability among parameters, and select one DGE to use. In applications, EDI-graphs confirm nonidentifiability in mixture models and in models parametrised with sums of parameters. EDI and PPVI explain why Tukey’s g-and-h model (DGE1) has better g-discrimination than the g-and-k model (DGE2), unless the sample size is extremely large; h_0 = k_0. EDIgraphs indicate that Normal learning machines have better parameter discrimination thanSigmoid learning machines and their parameters are non-identifiable.

A major challenge for ridesharing platforms is to guarantee profit and fairness simultaneously, especially in the presence of misaligned incentives of drivers and riders. We focus on the dispatchingpricing problem to maximize the total revenue while keeping both drivers and riders satisfied. We study the computational complexity of the problem, provide a novel two-phased pricing solution with revenue and fairness guarantees, extend it to stochastic settings and develop a dynamic (a.k.a., learning-while-doing) algorithm that actively collects data to learn the demand distribution during the scheduling process. We also conduct extensive experiments to demonstrate the effectiveness of our algorithms.

A human does not have to see all elephants to recognize an animal as an elephant. On contrast, current state-of-the-art deep learning approaches heavily depend on the variety of training samples and the capacity of the network. In practice, the size of network is always limited and it is impossible to access all the data samples. Under this circumstance, deep learning models are extremely fragile to human-imperceivable adversarial examples, which impose threats to all safety critical systems. Inspired by the association and attention mechanisms of the human brain, we propose reverse adversarial examples method that can greatly improve models' robustness on unseen data. Experiments show that our reverse adversarial method can improve accuracy on average 19.02% on ResNet18, MobileNet, and VGG16 on unseen data transformation. Besides, the proposed method is also applicable to compressed models and shows potential to compensate the robustness drop brought by model quantization - an absolute 30.78% accuracy improvement.

In recent years, how to learn a dictionary from input images for sparse modelling has been one very active topic in image processing and recognition. Most existing dictionary learning methods consider an over-complete dictionary, e.g. the K-SVD method. Often they require solving some minimization problem that is very challenging in terms of computational feasibility and efficiency. However, if the correlations among dictionary atoms are not well constrained, the redundancy of the dictionary does not necessarily improve the performance of sparse coding. This paper proposed a fast orthogonal dictionary learning method for sparse image representation. With comparable performance on several image restoration tasks, the proposed method is much more computationally efficient than the over-complete dictionary based learning methods.

Sparse coding and dictionary learning have seen their applications in many vision tasks, which usually is formulated as a non-convex optimization problem. Many iterative methods have been proposed to tackle such an optimization problem. However, it remains an open problem to have a method that is not only practically fast but also is globally convergent. In this paper, we proposed a fast proximal method for solving \ell_0 norm based dictionary learning problems, and we proved that the whole sequence generated by the proposed method converges to a stationary point with sub-linear convergence rate. The benefit of having a fast and convergent dictionary learning method is demonstrated in the applications of image recovery and face recognition.

Recently, sparse coding has been widely used in many applications ranging from image recovery to pattern recognition. The low mutual coherence of a dictionary is an important property that ensures the optimality of the sparse code generated from this dictionary. Indeed, most existing dictionary learning methods for sparse coding either implicitly or explicitly tried to learn an incoherent dictionary, which requires solving a very challenging non-convex optimization problem. In this paper, we proposed a hybrid alternating proximal algorithm for incoherent dictionary learning, and established its global convergence property. Such a convergent incoherent dictionary learning method is not only of theoretical interest, but also might benefit many sparse coding based applications.

Most existing dictionary learning algorithms consider a linear sparse model, which often cannot effectively characterize the nonlinear properties present in many types of visual data, e.g. dynamic texture (DT). Such nonlinear properties can be exploited by the so-called kernel sparse coding. This paper proposed an equiangular kernel dictionary learning method with optimal mutual coherence to exploit the nonlinear sparsity of high-dimensional visual data. Two main issues are addressed in the proposed method: (1) coding stability for redundant dictionary of infinite-dimensional space; and (2) computational efficiency for computing kernel matrix of training samples of high-dimensional data. The proposed kernel sparse coding method is applied to dynamic texture analysis with both local DT pattern extraction and global DT pattern characterization. The experimental results showed its performance gain over existing methods.