Ji Xu

Ji Xu, Gang Ren, Yao Xiao et al.

The centrality and diversity of the labeled data are very influential to the performance of semi-supervised learning (SSL), but most SSL models select the labeled data randomly. This study first construct a leading forest that forms a partially ordered topological space in an unsupervised way, and select a group of most representative samples to label with one shot (differs from active learning essentially) using property of homeomorphism. Then a kernelized large margin metric is efficiently learned for the selected data to classify the remaining unlabeled sample. Optimal leading forest (OLF) has been observed to have the advantage of revealing the difference evolution along a path within a subtree. Therefore, we formulate an optimization problem based on OLF to select the samples. Also with OLF, the multiple local metrics learning is facilitated to address multi-modal and mix-modal problem in SSL, especially when the number of class is large. Attribute to this novel design, stableness and accuracy of the performance is significantly improved when compared with the state-of-the-art graph SSL methods. The extensive experimental studies have shown that the proposed method achieved encouraging accuracy and efficiency. Code has been made available at https://github.com/alanxuji/DeLaLA.

Jinye Yang, Ji Xu, Di Wu et al.

Long-tailed (LT) classification is an unavoidable and challenging problem in the real world. Most existing long-tailed classification methods focus only on solving the class-wise imbalance while ignoring the attribute-wise imbalance. The deviation of a classification model is caused by both class-wise and attribute-wise imbalance. Due to the fact that attributes are implicit in most datasets and the combination of attributes is complex, attribute-wise imbalance is more difficult to handle. For this purpose, we proposed a novel long-tailed classification framework, aiming to build a multi-granularity classification model by means of invariant feature learning. This method first unsupervisedly constructs Coarse-Grained forest (CLF) to better characterize the distribution of attributes within a class. Depending on the distribution of attributes, one can customize suitable sampling strategies to construct different imbalanced datasets. We then introduce multi-center loss (MCL) that aims to gradually eliminate confusing attributes during feature learning process. The proposed framework does not necessarily couple to a specific LT classification model structure and can be integrated with any existing LT method as an independent component. Extensive experiments show that our approach achieves state-of-the-art performance on both existing benchmarks ImageNet-GLT and MSCOCO-GLT and can improve the performance of existing LT methods. Our codes are available on GitHub: \url{https://github.com/jinyery/cognisance}

Ji Xu, Yuan Xie, Wenchao Wang

Underwater acoustic target recognition is a challenging task owing to the intricate underwater environments and limited data availability. Insufficient data can hinder the ability of recognition systems to support complex modeling, thus impeding their advancement. To improve the generalization capacity of recognition models, techniques such as data augmentation have been employed to simulate underwater signals and diversify data distribution. However, the complexity of underwater environments can cause the simulated signals to deviate from real scenarios, resulting in biased models that are misguided by non-true data. In this study, we propose two strategies to enhance the generalization ability of models in the case of limited data while avoiding the risk of performance degradation. First, as an alternative to traditional data augmentation, we utilize smoothness-inducing regularization, which only incorporates simulated signals in the regularization term. Additionally, we propose a specialized spectrogram-based data augmentation strategy, namely local masking and replicating (LMR), to capture inter-class relationships. Our experiments and visualization analysis demonstrate the superiority of our proposed strategies.

Yuan Xie, Tianyu Chen, Ji Xu

Underwater acoustic recognition for ship-radiated signals has high practical application value due to the ability to recognize non-line-of-sight targets. However, due to the difficulty of data acquisition, the collected signals are scarce in quantity and mainly composed of mechanical periodic noise. According to the experiments, we observe that the repeatability of periodic signals leads to a double-descent phenomenon, which indicates a significant local bias toward repeated samples. To address this issue, we propose a strategy based on cross-entropy to prune excessively similar segments in training data. Furthermore, to compensate for the reduction of training data, we generate noisy samples and apply smoothness-inducing regularization based on KL divergence to mitigate overfitting. Experiments show that our proposed data pruning and regularization strategy can bring stable benefits and our framework significantly outperforms the state-of-the-art in low-resource scenarios.

Yao Xiao, Ji Xu, Jing Yang et al.

Graph Convolutional Networks (GCNs) have been proved successful in the field of semi-supervised node classification by extracting structural information from graph data. However, the random selection of labeled nodes used by GCNs may lead to unstable generalization performance of GCNs. In this paper, we propose an efficient method for the deterministic selection of labeled nodes: the Determinate Node Selection (DNS) algorithm. The DNS algorithm identifies two categories of representative nodes in the graph: typical nodes and divergent nodes. These labeled nodes are selected by exploring the structure of the graph and determining the ability of the nodes to represent the distribution of data within the graph. The DNS algorithm can be applied quite simply on a wide range of semi-supervised graph neural network models for node classification tasks. Through extensive experimentation, we have demonstrated that the incorporation of the DNS algorithm leads to a remarkable improvement in the average accuracy of the model and a significant decrease in the standard deviation, as compared to the original method.

Ji Xu, Tianlong Xiao, Jinye Yang et al.

Density peaks clustering (DP) has the ability of detecting clusters of arbitrary shape and clustering non-Euclidean space data, but its quadratic complexity in both computing and storage makes it difficult to scale for big data. Various approaches have been proposed in this regard, including MapReduce based distribution computing, multi-core parallelism, presentation transformation (e.g., kd-tree, Z-value), granular computing, and so forth. However, most of these existing methods face two limitations. One is their target datasets are mostly constrained to be in Euclidian space, the other is they emphasize only on local neighbors while ignoring global data distribution due to restriction to cut-off kernel when computing density. To address the two issues, we present a faithful and parallel DP method that makes use of two types of vector-like distance matrices and an inverse leading-node-finding policy. The method is implemented on a message passing interface (MPI) system. Extensive experiments showed that our method is capable of clustering non-Euclidean data such as in community detection, while outperforming the state-of-the-art counterpart methods in accuracy when clustering large Euclidean data. Our code is publicly available at https://github.com/alanxuji/FaithPDP.

Yuan Xie, Jiawei Ren, Junfeng Li et al.

Underwater acoustic target recognition has emerged as a prominent research area within the field of underwater acoustics. However, the current availability of authentic underwater acoustic signal recordings remains limited, which hinders data-driven acoustic recognition models from learning robust patterns of targets from a limited set of intricate underwater signals, thereby compromising their stability in practical applications. To overcome these limitations, this study proposes a recognition framework called M3 (Multi-task, Multi-gate, Multi-expert) to enhance the model's ability to capture robust patterns by making it aware of the inherent properties of targets. In this framework, an auxiliary task that focuses on target properties, such as estimating target size, is designed. The auxiliary task then shares parameters with the recognition task to realize multi-task learning. This paradigm allows the model to concentrate on shared information across tasks and identify robust patterns of targets in a regularized manner, thereby enhancing the model's generalization ability. Moreover, M3 incorporates multi-expert and multi-gate mechanisms, allowing for the allocation of distinct parameter spaces to various underwater signals. This enables the model to process intricate signal patterns in a fine-grained and differentiated manner. To evaluate the effectiveness of M3, extensive experiments were implemented on the ShipsEar underwater ship-radiated noise dataset. The results substantiate that M3 has the ability to outperform the most advanced single-task recognition models, thereby achieving the state-of-the-art performance.

Yuan Xie, Ji Xu, Jiawei Ren et al.

Underwater acoustic target recognition based on passive sonar faces numerous challenges in practical maritime applications. One of the main challenges lies in the susceptibility of signal characteristics to diverse environmental conditions and data acquisition configurations, which can lead to instability in recognition systems. While significant efforts have been dedicated to addressing these influential factors in other domains of underwater acoustics, they are often neglected in the field of underwater acoustic target recognition. To overcome this limitation, this study designs auxiliary tasks that model influential factors (e.g., source range, water column depth, or wind speed) based on available annotations and adopts a multi-task framework to connect these factors to the recognition task. Furthermore, we integrate an adversarial learning mechanism into the multi-task framework to prompt the model to extract representations that are robust against influential factors. Through extensive experiments and analyses on the ShipsEar dataset, our proposed adversarial multi-task model demonstrates its capacity to effectively model the influential factors and achieve state-of-the-art performance on the 12-class recognition task.

Yuan Xie, Xiaowei Zhang, Jiawei Ren et al.

Building a robust underwater acoustic recognition system in real-world scenarios is challenging due to the complex underwater environment and the dynamic motion states of targets. A promising optimization approach is to leverage the intrinsic physical characteristics of targets, which remain invariable regardless of environmental conditions, to provide robust insights. However, our study reveals that while physical characteristics exhibit robust properties, they may lack class-specific discriminative patterns. Consequently, directly incorporating physical characteristics into model training can potentially introduce unintended inductive biases, leading to performance degradation. To utilize the benefits of physical characteristics while mitigating possible detrimental effects, we propose DEMONet in this study, which utilizes the detection of envelope modulation on noise (DEMON) to provide robust insights into the shaft frequency or blade counts of targets. DEMONet is a multi-expert network that allocates various underwater signals to their best-matched expert layer based on DEMON spectra for fine-grained signal processing. Thereinto, DEMON spectra are solely responsible for providing implicit physical characteristics without establishing a mapping relationship with the target category. Furthermore, to mitigate noise and spurious modulation spectra in DEMON features, we introduce a cross-temporal alignment strategy and employ a variational autoencoder (VAE) to reconstruct noise-resistant DEMON spectra to replace the raw DEMON features. The effectiveness of the proposed DEMONet with cross-temporal VAE was primarily evaluated on the DeepShip dataset and our proprietary datasets. Experimental results demonstrated that our approach could achieve state-of-the-art performance on both datasets.

Wei Zhou, Peng Sun, Xuanhe Zhou et al.

The operation and maintenance (O&M) of database systems is critical to ensuring system availability and performance, typically requiring expert experience (e.g., identifying metric-to-anomaly relations) for effective diagnosis and recovery. However, existing automatic database O&M methods, including commercial products, cannot effectively utilize expert experience. On the one hand, rule-based methods only support basic O&M tasks (e.g., metric-based anomaly detection), which are mostly numerical equations and cannot effectively incorporate literal O&M experience (e.g., troubleshooting guidance in manuals). On the other hand, LLM-based methods, which retrieve fragmented information (e.g., standard documents + RAG), often generate inaccurate or generic results. To address these limitations, we present DBAIOps, a novel hybrid database O&M system that combines reasoning LLMs with knowledge graphs to achieve DBA-style diagnosis. First, DBAIOps introduces a heterogeneous graph model for representing the diagnosis experience, and proposes a semi-automatic graph construction algorithm to build that graph from thousands of documents. Second, DBAIOps develops a collection of (800+) reusable anomaly models that identify both directly alerted metrics and implicitly correlated experience and metrics. Third, for each anomaly, DBAIOps proposes a two-stage graph evolution mechanism to explore relevant diagnosis paths and identify missing relations automatically. It then leverages a reasoning LLM (e.g., DeepSeek-R1) to infer root causes and generate clear diagnosis reports for both DBAs and common users. Our evaluation over four mainstream database systems (Oracle, MySQL, PostgreSQL, and DM8) demonstrates that DBAIOps outperforms state-of-the-art baselines, 34.85% and 47.22% higher in root cause and human evaluation accuracy, respectively.

Bozhi Dan, Di Wu, Ji Xu et al.

In the intensive care setting, sepsis continues to be a major contributor to patient illness and death; however, its timely detection is hindered by the complex, sparse, and heterogeneous nature of electronic health record (EHR) data. We propose Triplet-GCN, a single-branch graph convolutional model that represents each encounter as patient-feature-value triplets, constructs a bipartite EHR graph, and learns patient embeddings via a Graph Convolutional Network (GCN) followed by a lightweight multilayer perceptron (MLP). The pipeline applies type-specific preprocessing -- median imputation and standardization for numeric variables, effect coding for binary features, and mode imputation with low-dimensional embeddings for rare categorical attributes -- and initializes patient nodes with summary statistics, while retaining measurement values on edges to preserve "who measured what and by how much". In a retrospective, multi-center Chinese cohort (N = 648; 70/30 train-test split) drawn from three tertiary hospitals, Triplet-GCN consistently outperforms strong tabular baselines (KNN, SVM, XGBoost, Random Forest) across discrimination and balanced error metrics, yielding a more favorable sensitivity-specificity trade-off and improved overall utility for early warning. These findings indicate that encoding EHR as triplets and propagating information over a patient-feature graph produce more informative patient representations than feature-independent models, offering a simple, end-to-end blueprint for deployable sepsis risk stratification.

Hejiang Cai, Di Wu, Ji Xu et al.

Sepsis is a life threatening condition that requires timely detection in intensive care settings. Traditional machine learning approaches, including Naive Bayes, Support Vector Machine (SVM), Random Forest, and XGBoost, often rely on manual feature engineering and struggle with irregular, incomplete time-series data commonly present in electronic health records. We introduce an end-to-end deep learning framework integrating an unsupervised autoencoder for automatic feature extraction with a multilayer perceptron classifier for binary sepsis risk prediction. To enhance clinical applicability, we implement a customized down sampling strategy that extracts high information density segments during training and a non-overlapping dynamic sliding window mechanism for real-time inference. Preprocessed time series data are represented as fixed dimension vectors with explicit missingness indicators, mitigating bias and noise. We validate our approach on three ICU cohorts. Our end-to-end model achieves accuracies of 74.6 percent, 80.6 percent, and 93.5 percent, respectively, consistently outperforming traditional machine learning baselines. These results demonstrate the framework's superior robustness, generalizability, and clinical utility for early sepsis detection across heterogeneous ICU environments.

Yuan Xie, Jiawei Ren, Ji Xu

Underwater acoustic target recognition is an intractable task due to the complex acoustic source characteristics and sound propagation patterns. Limited by insufficient data and narrow information perspective, recognition models based on deep learning seem far from satisfactory in practical underwater scenarios. Although underwater acoustic signals are severely influenced by distance, channel depth, or other factors, annotations of relevant information are often non-uniform, incomplete, and hard to use. In our work, we propose to implement Underwater Acoustic Recognition based on Templates made up of rich relevant information (hereinafter called "UART"). We design templates to integrate relevant information from different perspectives into descriptive natural language. UART adopts an audio-spectrogram-text tri-modal contrastive learning framework, which endows UART with the ability to guide the learning of acoustic representations by descriptive natural language. Our experiments reveal that UART has better recognition capability and generalization performance than traditional paradigms. Furthermore, the pre-trained UART model could provide superior prior knowledge for the recognition model in the scenario without any auxiliary annotation.

Yuan Xie, Jiawei Ren, Ji Xu

Analyzing the ocean acoustic environment is a tricky task. Background noise and variable channel transmission environment make it complicated to implement accurate ship-radiated noise recognition. Existing recognition systems are weak in addressing the variable underwater environment, thus leading to disappointing performance in practical application. In order to keep the recognition system robust in various underwater environments, this work proposes an adaptive generalized recognition system - AGNet (Adaptive Generalized Network). By converting fixed wavelet parameters into fine-grained learnable parameters, AGNet learns the characteristics of underwater sound at different frequencies. Its flexible and fine-grained design is conducive to capturing more background acoustic information (e.g., background noise, underwater transmission channel). To utilize the implicit information in wavelet spectrograms, AGNet adopts the convolutional neural network with parallel convolution attention modules as the classifier. Experiments reveal that our AGNet outperforms all baseline methods on several underwater acoustic datasets, and AGNet could benefit more from transfer learning. Moreover, AGNet shows robust performance against various interference factors.

Zehui Yang, Yifan Chen, Lei Luo et al.

This paper introduces a high-quality rich annotated Mandarin conversational (RAMC) speech dataset called MagicData-RAMC. The MagicData-RAMC corpus contains 180 hours of conversational speech data recorded from native speakers of Mandarin Chinese over mobile phones with a sampling rate of 16 kHz. The dialogs in MagicData-RAMC are classified into 15 diversified domains and tagged with topic labels, ranging from science and technology to ordinary life. Accurate transcription and precise speaker voice activity timestamps are manually labeled for each sample. Speakers' detailed information is also provided. As a Mandarin speech dataset designed for dialog scenarios with high quality and rich annotations, MagicData-RAMC enriches the data diversity in the Mandarin speech community and allows extensive research on a series of speech-related tasks, including automatic speech recognition, speaker diarization, topic detection, keyword search, text-to-speech, etc. We also conduct several relevant tasks and provide experimental results to help evaluate the dataset.

Keqi Deng, Songjun Cao, Yike Zhang et al.

Recently, end-to-end automatic speech recognition models based on connectionist temporal classification (CTC) have achieved impressive results, especially when fine-tuned from wav2vec2.0 models. Due to the conditional independence assumption, CTC-based models are always weaker than attention-based encoder-decoder models and require the assistance of external language models (LMs). To solve this issue, we propose two knowledge transferring methods that leverage pre-trained LMs, such as BERT and GPT2, to improve CTC-based models. The first method is based on representation learning, in which the CTC-based models use the representation produced by BERT as an auxiliary learning target. The second method is based on joint classification learning, which combines GPT2 for text modeling with a hybrid CTC/attention architecture. Experiment on AISHELL-1 corpus yields a character error rate (CER) of 4.2% on the test set. When compared to the vanilla CTC-based models fine-tuned from the wav2vec2.0 models, our knowledge transferring method reduces CER by 16.1% relatively without external LMs.

Junjie Ma, Ji Xu, Arian Maleki

We consider an inverse problem $\mathbf{y}= f(\mathbf{Ax})$, where $\mathbf{x}\in\mathbb{R}^n$ is the signal of interest, $\mathbf{A}$ is the sensing matrix, $f$ is a nonlinear function and $\mathbf{y} \in \mathbb{R}^m$ is the measurement vector. In many applications, we have some level of freedom to design the sensing matrix $\mathbf{A}$, and in such circumstances we could optimize $\mathbf{A}$ to achieve better reconstruction performance. As a first step towards optimal design, it is important to understand the impact of the sensing matrix on the difficulty of recovering $\mathbf{x}$ from $\mathbf{y}$. In this paper, we study the performance of one of the most successful recovery methods, i.e., the expectation propagation (EP) algorithm. We define a notion of spikiness for the spectrum of $\bmmathbfA}$ and show the importance of this measure for the performance of EP. We show that whether a spikier spectrum can hurt or help the recovery performance depends on $f$. Based on our framework, we are able to show that, in phase-retrieval problems, matrices with spikier spectrums are better for EP, while in 1-bit compressed sensing problems, less spiky spectrums lead to better performance. Our results unify and substantially generalize existing results that compare Gaussian and orthogonal matrices, and provide a platform towards designing optimal sensing systems.

Daniel Hsu, Vidya Muthukumar, Ji Xu

The support vector machine (SVM) is a well-established classification method whose name refers to the particular training examples, called support vectors, that determine the maximum margin separating hyperplane. The SVM classifier is known to enjoy good generalization properties when the number of support vectors is small compared to the number of training examples. However, recent research has shown that in sufficiently high-dimensional linear classification problems, the SVM can generalize well despite a proliferation of support vectors where all training examples are support vectors. In this paper, we identify new deterministic equivalences for this phenomenon of support vector proliferation, and use them to (1) substantially broaden the conditions under which the phenomenon occurs in high-dimensional settings, and (2) prove a nearly matching converse result.

Shun-ichi Amari, Jimmy Ba, Roger Grosse et al.

While second order optimizers such as natural gradient descent (NGD) often speed up optimization, their effect on generalization has been called into question. This work presents a more nuanced view on how the \textit{implicit bias} of first- and second-order methods affects the comparison of generalization properties. We provide an exact asymptotic bias-variance decomposition of the generalization error of overparameterized ridgeless regression under a general class of preconditioner $\boldsymbol{P}$, and consider the inverse population Fisher information matrix (used in NGD) as a particular example. We determine the optimal $\boldsymbol{P}$ for both the bias and variance, and find that the relative generalization performance of different optimizers depends on the label noise and the "shape" of the signal (true parameters): when the labels are noisy, the model is misspecified, or the signal is misaligned with the features, NGD can achieve lower risk; conversely, GD generalizes better than NGD under clean labels, a well-specified model, or aligned signal. Based on this analysis, we discuss several approaches to manage the bias-variance tradeoff, and the potential benefit of interpolating between GD and NGD. We then extend our analysis to regression in the reproducing kernel Hilbert space and demonstrate that preconditioned GD can decrease the population risk faster than GD. Lastly, we empirically compare the generalization error of first- and second-order optimizers in neural network experiments, and observe robust trends matching our theoretical analysis.

Denny Wu, Ji Xu

We consider the linear model $\mathbf{y} = \mathbf{X} \mathbfβ_\star + \mathbfε$ with $\mathbf{X}\in \mathbb{R}^{n\times p}$ in the overparameterized regime $p>n$. We estimate $\mathbfβ_\star$ via generalized (weighted) ridge regression: $\hat{\mathbfβ}_λ= \left(\mathbf{X}^T\mathbf{X} + λ\mathbfΣ_w\right)^\dagger \mathbf{X}^T\mathbf{y}$, where $\mathbfΣ_w$ is the weighting matrix. Under a random design setting with general data covariance $\mathbfΣ_x$ and anisotropic prior on the true coefficients $\mathbb{E}\mathbfβ_\star\mathbfβ_\star^T = \mathbfΣ_β$, we provide an exact characterization of the prediction risk $\mathbb{E}(y-\mathbf{x}^T\hat{\mathbfβ}_λ)^2$ in the proportional asymptotic limit $p/n\rightarrow γ\in (1,\infty)$. Our general setup leads to a number of interesting findings. We outline precise conditions that decide the sign of the optimal setting $λ_{\rm opt}$ for the ridge parameter $λ$ and confirm the implicit $\ell_2$ regularization effect of overparameterization, which theoretically justifies the surprising empirical observation that $λ_{\rm opt}$ can be negative in the overparameterized regime. We also characterize the double descent phenomenon for principal component regression (PCR) when both $\mathbf{X}$ and $\mathbfβ_\star$ are anisotropic. Finally, we determine the optimal weighting matrix $\mathbfΣ_w$ for both the ridgeless ($λ\to 0$) and optimally regularized ($λ= λ_{\rm opt}$) case, and demonstrate the advantage of the weighted objective over standard ridge regression and PCR.

Jingyu Yang, Ji Xu, Kun Li et al.

This paper proposes a new method for simultaneous 3D reconstruction and semantic segmentation of indoor scenes. Unlike existing methods that require recording a video using a color camera and/or a depth camera, our method only needs a small number of (e.g., 3-5) color images from uncalibrated sparse views as input, which greatly simplifies data acquisition and extends applicable scenarios. Since different views have limited overlaps, our method allows a single image as input to discern the depth and semantic information of the scene. The key issue is how to recover relatively accurate depth from single images and reconstruct a 3D scene by fusing very few depth maps. To address this problem, we first design an iterative deep architecture, IterNet, that estimates depth and semantic segmentation alternately, so that they benefit each other. To deal with the little overlap and non-rigid transformation between views, we further propose a joint global and local registration method to reconstruct a 3D scene with semantic information from sparse views. We also make available a new indoor synthetic dataset simultaneously providing photorealistic high-resolution RGB images, accurate depth maps and pixel-level semantic labels for thousands of complex layouts, useful for training and evaluation. Experimental results on public datasets and our dataset demonstrate that our method achieves more accurate depth estimation, smaller semantic segmentation errors and better 3D reconstruction results, compared with state-of-the-art methods.

Ji Xu, Daniel Hsu

We study least squares linear regression over $N$ uncorrelated Gaussian features that are selected in order of decreasing variance. When the number of selected features $p$ is at most the sample size $n$, the estimator under consideration coincides with the principal component regression estimator; when $p>n$, the estimator is the least $\ell_2$ norm solution over the selected features. We give an average-case analysis of the out-of-sample prediction error as $p,n,N \to \infty$ with $p/N \to α$ and $n/N \to β$, for some constants $α\in [0,1]$ and $β\in (0,1)$. In this average-case setting, the prediction error exhibits a "double descent" shape as a function of $p$. We also establish conditions under which the minimum risk is achieved in the interpolating ($p>n$) regime.

Mikhail Belkin, Daniel Hsu, Ji Xu

The "double descent" risk curve was proposed to qualitatively describe the out-of-sample prediction accuracy of variably-parameterized machine learning models. This article provides a precise mathematical analysis for the shape of this curve in two simple data models with the least squares/least norm predictor. Specifically, it is shown that the risk peaks when the number of features $p$ is close to the sample size $n$, but also that the risk decreases towards its minimum as $p$ increases beyond $n$. This behavior is contrasted with that of "prescient" models that select features in an a priori optimal order.

Ji Xu, Arian Maleki, Kamiar Rahnama Rad et al.

Risk estimation is at the core of many learning systems. The importance of this problem has motivated researchers to propose different schemes, such as cross validation, generalized cross validation, and Bootstrap. The theoretical properties of such estimates have been extensively studied in the low-dimensional settings, where the number of predictors $p$ is much smaller than the number of observations $n$. However, a unifying methodology accompanied with a rigorous theory is lacking in high-dimensional settings. This paper studies the problem of risk estimation under the moderately high-dimensional asymptotic setting $n,p \rightarrow \infty$ and $n/p \rightarrow δ>1$ ($δ$ is a fixed number), and proves the consistency of three risk estimates that have been successful in numerical studies, i.e., leave-one-out cross validation (LOOCV), approximate leave-one-out (ALO), and approximate message passing (AMP)-based techniques. A corner stone of our analysis is a bound that we obtain on the discrepancy of the `residuals' obtained from AMP and LOOCV. This connection not only enables us to obtain a more refined information on the estimates of AMP, ALO, and LOOCV, but also offers an upper bound on the convergence rate of each estimate.

Ji Xu, Daniel Hsu, Arian Maleki

Expectation Maximization (EM) is among the most popular algorithms for maximum likelihood estimation, but it is generally only guaranteed to find its stationary points of the log-likelihood objective. The goal of this article is to present theoretical and empirical evidence that over-parameterization can help EM avoid spurious local optima in the log-likelihood. We consider the problem of estimating the mean vectors of a Gaussian mixture model in a scenario where the mixing weights are known. Our study shows that the global behavior of EM, when one uses an over-parameterized model in which the mixing weights are treated as unknown, is better than that when one uses the (correct) model with the mixing weights fixed to the known values. For symmetric Gaussians mixtures with two components, we prove that introducing the (statistically redundant) weight parameters enables EM to find the global maximizer of the log-likelihood starting from almost any initial mean parameters, whereas EM without this over-parameterization may very often fail. For other Gaussian mixtures, we provide empirical evidence that shows similar behavior. Our results corroborate the value of over-parameterization in solving non-convex optimization problems, previously observed in other domains.

Ji Xu, Guoyin Wang

Graph based semi-supervised learning (GSSL) has intuitive representation and can be improved by exploiting the matrix calculation. However, it has to perform iterative optimization to achieve a preset objective, which usually leads to low efficiency. Another inconvenience lying in GSSL is that when new data come, the graph construction and the optimization have to be conducted all over again. We propose a sound assumption, arguing that: the neighboring data points are not in peer-to-peer relation, but in a partial-ordered relation induced by the local density and distance between the data; and the label of a center can be regarded as the contribution of its followers. Starting from the assumption, we develop a highly efficient non-iterative label propagation algorithm based on a novel data structure named as optimal leading forest (LaPOLeaF). The major weaknesses of the traditional GSSL are addressed by this study. We further scale LaPOLeaF to accommodate big data by utilizing block distance matrix technique, parallel computing, and Locality-Sensitive Hashing (LSH). Experiments on large datasets have shown the promising results of the proposed methods.

Lu Huang, Jiasong Sun, Ji Xu et al.

Long Short-Term Memory (LSTM) is the primary recurrent neural networks architecture for acoustic modeling in automatic speech recognition systems. Residual learning is an efficient method to help neural networks converge easier and faster. In this paper, we propose several types of residual LSTM methods for our acoustic modeling. Our experiments indicate that, compared with classic LSTM, our architecture shows more than 8% relative reduction in Phone Error Rate (PER) on TIMIT tasks. At the same time, our residual fast LSTM approach shows 4% relative reduction in PER on the same task. Besides, we find that all this architecture could have good results on THCHS-30, Librispeech and Switchboard corpora.

Ji Xu, Daniel Hsu, Arian Maleki

Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find stationary points of the likelihood objective, and these points may be far from any maximizer. This article addresses this disconnect between the statistical principles behind EM and its algorithmic properties. Specifically, it provides a global analysis of EM for specific models in which the observations comprise an i.i.d. sample from a mixture of two Gaussians. This is achieved by (i) studying the sequence of parameters from idealized execution of EM in the infinite sample limit, and fully characterizing the limit points of the sequence in terms of the initial parameters; and then (ii) based on this convergence analysis, establishing statistical consistency (or lack thereof) for the actual sequence of parameters produced by EM.

Ji Xu, Guoyin Wang

This paper reveals the tree structure as an intermediate result of clustering by fast search and find of density peaks (DPCLUS), and explores the power of using this tree to perform hierarchical clustering. The array used to hold the index of the nearest higher-densitied object for each object can be transformed into a Leading Tree (LT), in which each parent node P leads its child nodes to join the same cluster as P itself, and the child nodes are sorted by their gamma values in descendant order to accelerate the disconnecting of root in each subtree. There are two major advantages with the LT: One is dramatically reducing the running time of assigning noncenter data points to their cluster ID, because the assigning process is turned into just disconnecting the links from each center to its parent. The other is that the tree model for representing clusters is more informative. Because we can check which objects are more likely to be selected as centers in finer grained clustering, or which objects reach to its center via less jumps. Experiment results and analysis show the effectiveness and efficiency of the assigning process with an LT.