arXiv subjects

Jiaming Xu

Publications and source records attributed to Jiaming Xu.

At least 91 records · Page 5Linked to original sources

arXiv2020

Speaker-Conditional Chain Model for Speech Separation and Extraction

Speech separation has been extensively explored to tackle the cocktail party problem. However, these studies are still far from having enough generalization capabilities for real scenarios. In this work, we raise a common strategy named Speaker-Conditional Chain Model to process complex speech recordings. In the proposed method, our model first infers the identities of variable numbers of speakers from the observation based on a sequence-to-sequence model. Then, it takes the information from the inferred speakers as conditions to extract their speech sources. With the predicted speaker information from whole observation, our model is helpful to solve the problem of conventional speech separation and speaker extraction for multi-round long recordings. The experiments from standard fully-overlapped speech separation benchmarks show comparable results with prior studies, while our proposed model gets better adaptability for multi-round long recordings.

eess.AS↗

arXiv2020

Sequence to Multi-Sequence Learning via Conditional Chain Mapping for Mixture Signals

Neural sequence-to-sequence models are well established for applications which can be cast as mapping a single input sequence into a single output sequence. In this work, we focus on one-to-many sequence transduction problems, such as extracting multiple sequential sources from a mixture sequence. We extend the standard sequence-to-sequence model to a conditional multi-sequence model, which explicitly models the relevance between multiple output sequences with the probabilistic chain rule. Based on this extension, our model can conditionally infer output sequences one-by-one by making use of both input and previously-estimated contextual output sequences. This model additionally has a simple and efficient stop criterion for the end of the transduction, making it able to infer the variable number of output sequences. We take speech data as a primary test field to evaluate our methods since the observed speech data is often composed of multiple sources due to the nature of the superposition principle of sound waves. Experiments on several different tasks including speech separation and multi-speaker speech recognition show that our conditional multi-sequence models lead to consistent improvements over the conventional non-conditional models.

eess.AS↗

arXiv2019

All-or-Nothing Phenomena: From Single-Letter to High Dimensions

We consider the linear regression problem of estimating a $p$-dimensional vector $β$ from $n$ observations $Y = X β+ W$, where $β_j \stackrel{\text{i.i.d.}}{\sim} π$ for a real-valued distribution $π$ with zero mean and unit variance, $X_{ij} \stackrel{\text{i.i.d.}}{\sim} \mathcal{N}(0,1)$, and $W_i\stackrel{\text{i.i.d.}}{\sim} \mathcal{N}(0, σ^2)$. In the asymptotic regime where $n/p \to δ$ and $ p/ σ^2 \to \mathsf{snr}$ for two fixed constants $δ, \mathsf{snr}\in (0, \infty)$ as $p \to \infty$, the limiting (normalized) minimum mean-squared error (MMSE) has been characterized by the MMSE of an associated single-letter (additive Gaussian scalar) channel. In this paper, we show that if the MMSE function of the single-letter channel converges to a step function, then the limiting MMSE of estimating $β$ in the linear regression problem converges to a step function which jumps from $1$ to $0$ at a critical threshold. Moreover, we establish that the limiting mean-squared error of the (MSE-optimal) approximate message passing algorithm also converges to a step function with a larger threshold, providing evidence for the presence of a computational-statistical gap between the two thresholds.

math.ST↗

arXiv2019

DMRM: A Dual-channel Multi-hop Reasoning Model for Visual Dialog

Visual Dialog is a vision-language task that requires an AI agent to engage in a conversation with humans grounded in an image. It remains a challenging task since it requires the agent to fully understand a given question before making an appropriate response not only from the textual dialog history, but also from the visually-grounded information. While previous models typically leverage single-hop reasoning or single-channel reasoning to deal with this complex multimodal reasoning task, which is intuitively insufficient. In this paper, we thus propose a novel and more powerful Dual-channel Multi-hop Reasoning Model for Visual Dialog, named DMRM. DMRM synchronously captures information from the dialog history and the image to enrich the semantic representation of the question by exploiting dual-channel reasoning. Specifically, DMRM maintains a dual channel to obtain the question- and history-aware image features and the question- and image-aware dialog history features by a mulit-hop reasoning process in each channel. Additionally, we also design an effective multimodal attention to further enhance the decoder to generate more accurate responses. Experimental results on the VisDial v0.9 and v1.0 datasets demonstrate that the proposed model is effective and outperforms compared models by a significant margin.

cs.CL↗

arXiv2019

Consistent recovery threshold of hidden nearest neighbor graphs

Motivated by applications such as discovering strong ties in social networks and assembling genome subsequences in biology, we study the problem of recovering a hidden $2k$-nearest neighbor (NN) graph in an $n$-vertex complete graph, whose edge weights are independent and distributed according to $P_n$ for edges in the hidden $2k$-NN graph and $Q_n$ otherwise. The special case of Bernoulli distributions corresponds to a variant of the Watts-Strogatz small-world graph. We focus on two types of asymptotic recovery guarantees as $n\to \infty$: (1) exact recovery: all edges are classified correctly with probability tending to one; (2) almost exact recovery: the expected number of misclassified edges is $o(nk)$. We show that the maximum likelihood estimator achieves (1) exact recovery for $2 \le k \le n^{o(1)}$ if $ \liminf \frac{2α_n}{\log n}>1$; (2) almost exact recovery for $ 1 \le k \le o\left( \frac{\log n}{\log \log n} \right)$ if $\liminf \frac{kD(P_n||Q_n)}{\log n}>1$, where $α_n \triangleq -2 \log \int \sqrt{d P_n d Q_n}$ is the Rényi divergence of order $\frac{1}{2}$ and $D(P_n||Q_n)$ is the Kullback-Leibler divergence. Under mild distributional assumptions, these conditions are shown to be information-theoretically necessary for any algorithm to succeed. A key challenge in the analysis is the enumeration of $2k$-NN graphs that differ from the hidden one by a given number of edges.

cs.DS↗

arXiv2019

Spectral Graph Matching and Regularized Quadratic Relaxations I: The Gaussian Model

Graph matching aims at finding the vertex correspondence between two unlabeled graphs that maximizes the total edge weight correlation. This amounts to solving a computationally intractable quadratic assignment problem. In this paper we propose a new spectral method, GRAph Matching by Pairwise eigen-Alignments (GRAMPA). Departing from prior spectral approaches that only compare top eigenvectors, or eigenvectors of the same order, GRAMPA first constructs a similarity matrix as a weighted sum of outer products between all pairs of eigenvectors of the two graphs, with weights given by a Cauchy kernel applied to the separation of the corresponding eigenvalues, then outputs a matching by a simple rounding procedure. The similarity matrix can also be interpreted as the solution to a regularized quadratic programming relaxation of the quadratic assignment problem. For the Gaussian Wigner model in which two complete graphs on $n$ vertices have Gaussian edge weights with correlation coefficient $1-σ^2$, we show that GRAMPA exactly recovers the correct vertex correspondence with high probability when $σ= O(\frac{1}{\log n})$. This matches the state of the art of polynomial-time algorithms, and significantly improves over existing spectral methods which require $σ$ to be polynomially small in $n$. The superiority of GRAMPA is also demonstrated on a variety of synthetic and real datasets, in terms of both statistical accuracy and computational efficiency. Universality results, including similar guarantees for dense and sparse Erdős-Rényi graphs, are deferred to the companion paper.

stat.ML↗

arXiv2019

Spectral Graph Matching and Regularized Quadratic Relaxations II: Erdős-Rényi Graphs and Universality

We analyze a new spectral graph matching algorithm, GRAph Matching by Pairwise eigen-Alignments (GRAMPA), for recovering the latent vertex correspondence between two unlabeled, edge-correlated weighted graphs. Extending the exact recovery guarantees established in the companion paper for Gaussian weights, in this work, we prove the universality of these guarantees for a general correlated Wigner model. In particular, for two Erdős-Rényi graphs with edge correlation coefficient $1-σ^2$ and average degree at least $\operatorname{polylog}(n)$, we show that GRAMPA exactly recovers the latent vertex correspondence with high probability when $σ\lesssim 1/\operatorname{polylog}(n)$. Moreover, we establish a similar guarantee for a variant of GRAMPA, corresponding to a tighter quadratic programming relaxation of the quadratic assignment problem. Our analysis exploits a resolvent representation of the GRAMPA similarity matrix and local laws for the resolvents of sparse Wigner matrices.

math.PR↗

arXiv2019

POG: Personalized Outfit Generation for Fashion Recommendation at Alibaba iFashion

Increasing demand for fashion recommendation raises a lot of challenges for online shopping platforms and fashion communities. In particular, there exist two requirements for fashion outfit recommendation: the Compatibility of the generated fashion outfits, and the Personalization in the recommendation process. In this paper, we demonstrate these two requirements can be satisfied via building a bridge between outfit generation and recommendation. Through large data analysis, we observe that people have similar tastes in individual items and outfits. Therefore, we propose a Personalized Outfit Generation (POG) model, which connects user preferences regarding individual items and outfits with Transformer architecture. Extensive offline and online experiments provide strong quantitative evidence that our method outperforms alternative methods regarding both compatibility and personalization metrics. Furthermore, we deploy POG on a platform named Dida in Alibaba to generate personalized outfits for the users of the online application iFashion. This work represents a first step towards an industrial-scale fashion outfit generation and recommendation solution, which goes beyond generating outfits based on explicit queries, or merely recommending from existing outfit pools. As part of this work, we release a large-scale dataset consisting of 1.01 million outfits with rich context information, and 0.28 billion user click actions from 3.57 million users. To the best of our knowledge, this dataset is the largest, publicly available, fashion related dataset, and the first to provide user behaviors relating to both outfits and fashion items.

cs.IR↗

arXiv2019

Securing Distributed Gradient Descent in High Dimensional Statistical Learning

We consider unreliable distributed learning systems wherein the training data is kept confidential by external workers, and the learner has to interact closely with those workers to train a model. In particular, we assume that there exists a system adversary that can adaptively compromise some workers; the compromised workers deviate from their local designed specifications by sending out arbitrarily malicious messages. We assume in each communication round, up to $q$ out of the $m$ workers suffer Byzantine faults. Each worker keeps a local sample of size $n$ and the total sample size is $N=nm$. We propose a secured variant of the gradient descent method that can tolerate up to a constant fraction of Byzantine workers, i.e., $q/m = O(1)$. Moreover, we show the statistical estimation error of the iterates converges in $O(\log N)$ rounds to $O(\sqrt{q/N} + \sqrt{d/N})$, where $d$ is the model dimension. As long as $q=O(d)$, our proposed algorithm achieves the optimal error rate $O(\sqrt{d/N})$. Our results are obtained under some technical assumptions. Specifically, we assume strongly-convex population risk. Nevertheless, the empirical risk (sample version) is allowed to be non-convex. The core of our method is to robustly aggregate the gradients computed by the workers based on the filtering procedure proposed by Steinhardt et al. On the technical front, deviating from the existing literature on robustly estimating a finite-dimensional mean vector, we establish a {\em uniform} concentration of the sample covariance matrix of gradients, and show that the aggregated gradient, as a function of model parameter, converges uniformly to the true gradient function. To get a near-optimal uniform concentration bound, we develop a new matrix concentration inequality, which might be of independent interest.

cs.DC↗

arXiv2019

The All-or-Nothing Phenomenon in Sparse Linear Regression

We study the problem of recovering a hidden binary $k$-sparse $p$-dimensional vector $β$ from $n$ noisy linear observations $Y=Xβ+W$ where $X_{ij}$ are i.i.d. $\mathcal{N}(0,1)$ and $W_i$ are i.i.d. $\mathcal{N}(0,σ^2)$. A closely related hypothesis testing problem is to distinguish the pair $(X,Y)$ generated from this structured model from a corresponding null model where $(X,Y)$ consist of purely independent Gaussian entries. In the low sparsity $k=o(p)$ and high signal to noise ratio $k/σ^2=Ω\left(1\right)$ regime, we establish an `All-or-Nothing' information-theoretic phase transition at a critical sample size $n^*=2 k\log \left(p/k\right) /\log \left(1+k/σ^2\right)$, resolving a conjecture of \cite{gamarnikzadik}. Specifically, we show that if $\liminf_{p\to \infty} n/n^*>1$, then the maximum likelihood estimator almost perfectly recovers the hidden vector with high probability and moreover the true hypothesis can be detected with a vanishing error probability. Conversely, if $\limsup_{p\to \infty} n/n^*<1$, then it becomes information-theoretically impossible even to recover an arbitrarily small but fixed fraction of the hidden vector support, or to test hypotheses strictly better than random guess. Our proof of the impossibility result builds upon two key techniques, which could be of independent interest. First, we use a conditional second moment method to upper bound the Kullback-Leibler (KL) divergence between the structured and the null model. Second, inspired by the celebrated area theorem, we establish a lower bound to the minimum mean squared estimation error of the hidden vector in terms of the KL divergence between the two models.

math.ST↗

arXiv2019

Improved queue-size scaling for input-queued switches via graph factorization

This paper studies the scaling of the expected total queue size in an $n\times n$ input-queued switch, as a function of both the load $ρ$ and the system scale $n$. We provide a new class of scheduling policies under which the expected total queue size scales as $O\left( n(1-ρ)^{-4/3} \log \left(\max\{\frac{1}{1-ρ}, n\}\right)\right)$, over all $n$ and $ρ<1$, when the arrival rates are uniform. This improves over the previously best-known scalings in two regimes: $O\left(n^{1.5}(1-ρ)^{-1} \log \frac{1}{1-ρ}\right)$ when $Ω(n^{-1.5}) \le 1-ρ\le O(n^{-1})$ and $O\left(\frac{n\log n}{(1-ρ)^2}\right)$ when $1-ρ\geq Ω(n^{-1})$. A key ingredient in our method is a tight characterization of the largest $k$-factor of a random bipartite multigraph, which may be of independent interest.

cs.NI↗

arXiv2018

Learning from Comparisons and Choices

When tracking user-specific online activities, each user's preference is revealed in the form of choices and comparisons. For example, a user's purchase history is a record of her choices, i.e. which item was chosen among a subset of offerings. A user's preferences can be observed either explicitly as in movie ratings or implicitly as in viewing times of news articles. Given such individualized ordinal data in the form of comparisons and choices, we address the problem of collaboratively learning representations of the users and the items. The learned features can be used to predict a user's preference of an unseen item to be used in recommendation systems. This also allows one to compute similarities among users and items to be used for categorization and search. Motivated by the empirical successes of the MultiNomial Logit (MNL) model in marketing and transportation, and also more recent successes in word embedding and crowdsourced image embedding, we pose this problem as learning the MNL model parameters that best explain the data. We propose a convex relaxation for learning the MNL model, and show that it is minimax optimal up to a logarithmic factor by comparing its performance to a fundamental lower bound. This characterizes the minimax sample complexity of the problem, and proves that the proposed estimator cannot be improved upon other than by a logarithmic factor. Further, the analysis identifies how the accuracy depends on the topology of sampling via the spectrum of the sampling graph. This provides a guideline for designing surveys when one can choose which items are to be compared. This is accompanied by numerical simulations on synthetic and real data sets, confirming our theoretical predictions.

stat.ML↗

arXiv2018

Concept Learning through Deep Reinforcement Learning with Memory-Augmented Neural Networks

Deep neural networks have shown superior performance in many regimes to remember familiar patterns with large amounts of data. However, the standard supervised deep learning paradigm is still limited when facing the need to learn new concepts efficiently from scarce data. In this paper, we present a memory-augmented neural network which is motivated by the process of human concept learning. The training procedure, imitating the concept formation course of human, learns how to distinguish samples from different classes and aggregate samples of the same kind. In order to better utilize the advantages originated from the human behavior, we propose a sequential process, during which the network should decide how to remember each sample at every step. In this sequential process, a stable and interactive memory serves as an important module. We validate our model in some typical one-shot learning tasks and also an exploratory outlier detection problem. In all the experiments, our model gets highly competitive to reach or outperform those strong baselines.

cs.LG↗

arXiv2018

Convex Relaxation Methods for Community Detection

This paper surveys recent theoretical advances in convex optimization approaches for community detection. We introduce some important theoretical techniques and results for establishing the consistency of convex community detection under various statistical models. In particular, we discuss the basic techniques based on the primal and dual analysis. We also present results that demonstrate several distinctive advantages of convex community detection, including robustness against outlier nodes, consistency under weak assortativity, and adaptivity to heterogeneous degrees. This survey is not intended to be a complete overview of the vast literature on this fast-growing topic. Instead, we aim to provide a big picture of the remarkable recent development in this area and to make the survey accessible to a broad audience. We hope that this expository article can serve as an introductory guide for readers who are interested in using, designing, and analyzing convex relaxation methods in network analysis.

math.ST↗

arXiv2018

Cascaded Mutual Modulation for Visual Reasoning

Visual reasoning is a special visual question answering problem that is multi-step and compositional by nature, and also requires intensive text-vision interactions. We propose CMM: Cascaded Mutual Modulation as a novel end-to-end visual reasoning model. CMM includes a multi-step comprehension process for both question and image. In each step, we use a Feature-wise Linear Modulation (FiLM) technique to enable textual/visual pipeline to mutually control each other. Experiments show that CMM significantly outperforms most related models, and reach state-of-the-arts on two visual reasoning benchmarks: CLEVR and NLVR, collected from both synthetic and natural languages. Ablation studies confirm that both our multistep framework and our visual-guided language modulation are critical to the task. Our code is available at https://github.com/FlamingHorizon/CMM-VR.

cs.IR↗

arXiv2018

Statistical Problems with Planted Structures: Information-Theoretical and Computational Limits

Over the past few years, insights from computer science, statistical physics, and information theory have revealed phase transitions in a wide array of high-dimensional statistical problems at two distinct thresholds: One is the information-theoretical (IT) threshold below which the observation is too noisy so that inference of the ground truth structure is impossible regardless of the computational cost; the other is the computational threshold above which inference can be performed efficiently, i.e., in time that is polynomial in the input size. In the intermediate regime, inference is information-theoretically possible, but conjectured to be computationally hard. This article provides a survey of the common techniques for determining the sharp IT and computational limits, using community detection and submatrix detection as illustrating examples. For IT limits, we discuss tools including the first and second moment method for analyzing the maximum likelihood estimator, information-theoretic methods for proving impossibility results using mutual information and rate-distortion theory, and methods originated from statistical physics such as interpolation method. To investigate computational limits, we describe a common recipe to construct a randomized polynomial-time reduction scheme that approximately maps instances of the planted clique problem to the problem of interest in total variation distance.

math.ST↗

arXiv2018

Seeded Graph Matching via Large Neighborhood Statistics

We study a well known noisy model of the graph isomorphism problem. In this model, the goal is to perfectly recover the vertex correspondence between two edge-correlated Erdős-Rényi random graphs, with an initial seed set of correctly matched vertex pairs revealed as side information. For seeded problems, our result provides a significant improvement over previously known results. We show that it is possible to achieve the information-theoretic limit of graph sparsity in time polynomial in the number of vertices $n$. Moreover, we show the number of seeds needed for exact recovery in polynomial-time can be as low as $n^{3ε}$ in the sparse graph regime (with the average degree smaller than $n^ε$) and $Ω(\log n)$ in the dense graph regime. Our results also shed light on the unseeded problem. In particular, we give sub-exponential time algorithms for sparse models and an $n^{O(\log n)}$ algorithm for dense models for some parameters, including some that are not covered by recent results of Barak et al.

cs.LG↗

arXiv2018

Hidden Hamiltonian Cycle Recovery via Linear Programming

We introduce the problem of hidden Hamiltonian cycle recovery, where there is an unknown Hamiltonian cycle in an $n$-vertex complete graph that needs to be inferred from noisy edge measurements. The measurements are independent and distributed according to $\calP_n$ for edges in the cycle and $\calQ_n$ otherwise. This formulation is motivated by a problem in genome assembly, where the goal is to order a set of contigs (genome subsequences) according to their positions on the genome using long-range linking measurements between the contigs. Computing the maximum likelihood estimate in this model reduces to a Traveling Salesman Problem (TSP). Despite the NP-hardness of TSP, we show that a simple linear programming (LP) relaxation, namely the fractional $2$-factor (F2F) LP, recovers the hidden Hamiltonian cycle with high probability as $n \to \infty$ provided that $α_n - \log n \to \infty$, where $α_n \triangleq -2 \log \int \sqrt{d P_n d Q_n}$ is the Rényi divergence of order $\frac{1}{2}$. This condition is information-theoretically optimal in the sense that, under mild distributional assumptions, $α_n \geq (1+o(1)) \log n$ is necessary for any algorithm to succeed regardless of the computational cost. Departing from the usual proof techniques based on dual witness construction, the analysis relies on the combinatorial characterization (in particular, the half-integrality) of the extreme points of the F2F polytope. Represented as bicolored multi-graphs, these extreme points are further decomposed into simpler "blossom-type" structures for the large deviation analysis and counting arguments. Evaluation of the algorithm on real data shows improvements over existing approaches.

cs.DM↗