arXiv subjects

Jingjing Wu

Publications and source records attributed to Jingjing Wu.

23 records · Page 2Linked to original sources

arXiv2023

Stochastic Gradient Descent in the Viewpoint of Graduated Optimization

Stochastic gradient descent (SGD) method is popular for solving non-convex optimization problems in machine learning. This work investigates SGD from a viewpoint of graduated optimization, which is a widely applied approach for non-convex optimization problems. Instead of the actual optimization problem, a series of smoothed optimization problems that can be achieved in various ways are solved in the graduated optimization approach. In this work, a formal formulation of the graduated optimization is provided based on the nonnegative approximate identity, which generalizes the idea of Gaussian smoothing. Also, an asymptotic convergence result is achieved with the techniques in variational analysis. Then, we show that the traditional SGD method can be applied to solve the smoothed optimization problem. The Monte Carlo integration is used to achieve the gradient in the smoothed problem, which may be consistent with distributed computing schemes in real-life applications. From the assumptions on the actual optimization problem, the convergence results of SGD for the smoothed problem can be derived straightforwardly. Numerical examples show evidence that the graduated optimization approach may provide more accurate training results in certain cases.

math.OC↗

arXiv2023

High Dimensional Quadratic Discriminant Analysis: Optimality and Phase Transitions

Consider a two-class classification problem where we observe samples $(X_i, Y_i)$ for i = 1, ..., n, $X_i \in R^p$ and $Y_i$ in {0, 1}. Given $Y_i = k$, $X_i$ is assumed to follow a multivariate normal distribution with mean $μ_k \in R^k$ and covariance matrix $Σ_k$, k=0,1. Supposing a new sample X from the same mixture is observed, our goal is to estimate its class label Y. Such a high-dimensional classification problem has been studied thoroughly when Sigma_0 = Sigma_1. However, the discussions over the case $Σ_0 \neq Σ_1$ are much less over the years. This paper presents the quadratic discriminant analysis (QDA) for the weak signals (QDAw) algorithm, and the QDA with feature selection (QDAfs) algorithm. QDAfs applies Partial Correlation Screening to estimate $\hatΩ_0$ and $\hatΩ_1$, and then applies a hard-thresholding on the diagonals of $\hatΩ_0 - \hatΩ_1$. QDAfs further includes the linear term $d^T X$, where d is achieved by a hard-thresholding on $\hatΩ_1\hatμ_1 - \hatΩ_0\hatμ_0$. We further propose the rare and weak model to model the signals in $Ω_0 - Ω_1$ and $μ_0 - μ_1$. Based on the signal weakness and sparsity in $μ_0 - μ_1$, we propose two ways to estimate labels: 1) QDAw for weak but dense signals; 2) QDAfs for relatively strong but sparse signals. We figure out the classification boundary on the 4-dim parameter space: 1) Region of possibility, where either QDAw or QDAfs will achieve a mis-classification error rate of 0; 2) Region of impossibility, where all classifiers will have a constant error rate. The numerical results from real datasets support our theories and demonstrate the necessity and superiority of using QDA over LDA for classification.

math.ST↗

arXiv2023

Single Shot Self-Reliant Scene Text Spotter by Decoupled yet Collaborative Detection and Recognition

Typical text spotters follow the two-stage spotting paradigm which detects the boundary for a text instance first and then performs text recognition within the detected regions. Despite the remarkable progress of such spotting paradigm, an important limitation is that the performance of text recognition depends heavily on the precision of text detection, resulting in the potential error propagation from detection to recognition. In this work, we propose the single shot Self-Reliant Scene Text Spotter v2 (SRSTS v2), which circumvents this limitation by decoupling recognition from detection while optimizing two tasks collaboratively. Specifically, our SRSTS v2 samples representative feature points around each potential text instance, and conducts both text detection and recognition in parallel guided by these sampled points. Thus, the text recognition is no longer dependent on detection, thereby alleviating the error propagation from detection to recognition. Moreover, the sampling module is learned under the supervision from both detection and recognition, which allows for the collaborative optimization and mutual enhancement between two tasks. Benefiting from such sampling-driven concurrent spotting framework, our approach is able to recognize the text instances correctly even if the precise text boundaries are challenging to detect. Extensive experiments on four benchmarks demonstrate that our method compares favorably to state-of-the-art spotters.

cs.CV↗

arXiv2018

Sufficient Dimension Reduction for Classification

We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and Zhong (2015), which measures the dependence between a categorical random variable with multiple classes and a continuous random variable. Our method requires reasonably mild restrictions on the predicting variables and keeps the model-free advantage without the need to estimate the link function. The consistency of the MMV estimator is established under regularity conditions for both fixed and diverging dimension (p) cases and the number of the response classes can also be allowed to diverge with the sample size n. We also construct the asymptotic normality for the estimator when the dimension of the predicting vector is fixed. Furthermore, our method works pretty well when n < p. The surprising classification efficiency gain of the proposed method is demonstrated by simulation studies and real data analysis.

stat.ME↗

arXiv2018

Sequence-based Person Attribute Recognition with Joint CTC-Attention Model

Attribute recognition has become crucial because of its wide applications in many computer vision tasks, such as person re-identification. Like many object recognition problems, variations in viewpoints, illumination, and recognition at far distance, all make this task challenging. In this work, we propose a joint CTC-Attention model (JCM), which maps attribute labels into sequences to learn the semantic relationship among attributes. Besides, this network uses neural network to encode images into sequences, and employs connectionist temporal classification (CTC) loss to train the network with the aim of improving the encoding performance of the network. At the same time, it adopts the attention model to decode the sequences, which can realize aligning the sequences and better learning the semantic information from attributes. Extensive experiments on three public datasets, i.e., Market-1501 attribute dataset, Duke attribute dataset and PETA dataset, demonstrate the effectiveness of the proposed method.

cs.CV↗