arXiv subjects

Yuheng Bu

Publications and source records attributed to Yuheng Bu.

59 records · Page 4Linked to original sources

arXiv2018

Model change detection with application to machine learning

Model change detection is studied, in which there are two sets of samples that are independently and identically distributed (i.i.d.) according to a pre-change probabilistic model with parameter $θ$, and a post-change model with parameter $θ'$, respectively. The goal is to detect whether the change in the model is significant, i.e., whether the difference between the pre-change parameter and the post-change parameter $\|θ-θ'\|_2$ is larger than a pre-determined threshold $ρ$. The problem is considered in a Neyman-Pearson setting, where the goal is to maximize the probability of detection under a false alarm constraint. Since the generalized likelihood ratio test (GLRT) is difficult to compute in this problem, we construct an empirical difference test (EDT), which approximates the GLRT and has low computational complexity. Moreover, we provide an approximation method to set the threshold of the EDT to meet the false alarm constraint. Experiments with linear regression and logistic regression are conducted to validate the proposed algorithms.

stat.ML↗

arXiv2018

Active and Adaptive Sequential learning

A framework is introduced for actively and adaptively solving a sequence of machine learning problems, which are changing in bounded manner from one time step to the next. An algorithm is developed that actively queries the labels of the most informative samples from an unlabeled data pool, and that adapts to the change by utilizing the information acquired in the previous steps. Our analysis shows that the proposed active learning algorithm based on stochastic gradient descent achieves a near-optimal excess risk performance for maximum likelihood estimation. Furthermore, an estimator of the change in the learning problems using the active learning samples is constructed, which provides an adaptive sample size selection rule that guarantees the excess risk is bounded for sufficiently large number of time steps. Experiments with synthetic and real data are presented to validate our algorithm and theoretical results.

cs.LG↗

arXiv2018

Estimation of KL Divergence: Optimal Minimax Rate

The problem of estimating the Kullback-Leibler divergence $D(P\|Q)$ between two unknown distributions $P$ and $Q$ is studied, under the assumption that the alphabet size $k$ of the distributions can scale to infinity. The estimation is based on $m$ independent samples drawn from $P$ and $n$ independent samples drawn from $Q$. It is first shown that there does not exist any consistent estimator that guarantees asymptotically small worst-case quadratic risk over the set of all pairs of distributions. A restricted set that contains pairs of distributions, with density ratio bounded by a function $f(k)$ is further considered. {An augmented plug-in estimator is proposed, and its worst-case quadratic risk is shown to be within a constant factor of $(\frac{k}{m}+\frac{kf(k)}{n})^2+\frac{\log ^2 f(k)}{m}+\frac{f(k)}{n}$, if $m$ and $n$ exceed a constant factor of $k$ and $kf(k)$, respectively.} Moreover, the minimax quadratic risk is characterized to be within a constant factor of $(\frac{k}{m\log k}+\frac{kf(k)}{n\log k})^2+\frac{\log ^2 f(k)}{m}+\frac{f(k)}{n}$, if $m$ and $n$ exceed a constant factor of $k/\log(k)$ and $kf(k)/\log k$, respectively. The lower bound on the minimax quadratic risk is characterized by employing a generalized Le Cam's method. A minimax optimal estimator is then constructed by employing both the polynomial approximation and the plug-in approaches.

cs.IT↗

arXiv2017

Linear-Complexity Exponentially-Consistent Tests for Universal Outlying Sequence Detection

The problem of universal outlying sequence detection is studied, where the goal is to detect outlying sequences among $M$ sequences of samples. A sequence is considered as outlying if the observations therein are generated by a distribution different from those generating the observations in the majority of the sequences. In the universal setting, we are interested in identifying all the outlying sequences without knowing the underlying generating distributions. In this paper, a class of tests based on distribution clustering is proposed. These tests are shown to be exponentially consistent with linear time complexity in $M$. Numerical results demonstrate that our clustering-based tests achieve similar performance to existing tests, while being considerably more computationally efficient.

cs.IT↗

arXiv2015

Universal Outlying sequence detection For Continuous Observations

The following detection problem is studied, in which there are $M$ sequences of samples out of which one outlier sequence needs to be detected. Each typical sequence contains $n$ independent and identically distributed (i.i.d.) continuous observations from a known distribution $π$, and the outlier sequence contains $n$ i.i.d. observations from an outlier distribution $μ$, which is distinct from $π$, but otherwise unknown. A universal test based on KL divergence is built to approximate the maximum likelihood test, with known $π$ and unknown $μ$. A data-dependent partitions based KL divergence estimator is employed. Such a KL divergence estimator is further shown to converge to its true value exponentially fast when the density ratio satisfies $0<K_1\leq \frac{dμ}{dπ}\leq K_2$, where $K_1$ and $K_2$ are positive constants, and this further implies that the test is exponentially consistent. The performance of the test is compared with that of a recently introduced test for this problem based on the machine learning approach of maximum mean discrepancy (MMD). We identify regimes in which the KL divergence based test is better than the MMD based test.

cs.IT↗