arXiv subjects

Yi Li

Publications and source records attributed to Yi Li.

At least 541 records · Page 30Linked to original sources

arXiv2018

Matrix Norms in Data Streams: Faster, Multi-Pass and Row-Order

A central problem in data streams is to characterize which functions of an underlying frequency vector can be approximated efficiently. Recently there has been considerable effort in extending this problem to that of estimating functions of a matrix that is presented as a data-stream. This setting generalizes classical problems to the analogous ones for matrices. For example, instead of estimating frequent-item counts, we now wish to estimate "frequent-direction" counts. A related example is to estimate norms, which now correspond to estimating a vector norm on the singular values of the matrix. Despite recent efforts, the current understanding for such matrix problems is considerably weaker than that for vector problems. We study a number of aspects of estimating matrix norms in a stream that have not previously been considered: (1) multi-pass algorithms, (2) algorithms that see the underlying matrix one row at a time, and (3) time-efficient algorithms. Our multi-pass and row-order algorithms use less memory than what is provably required in the single-pass and entrywise-update models, and thus give separations between these models (in terms of memory). Moreover, all of our algorithms are considerably faster than previous ones. We also prove a number of lower bounds, and obtain for instance, a near-complete characterization of the memory required of row-order algorithms for estimating Schatten $p$-norms of sparse matrices.

cs.DS↗

arXiv2018

Local curvature estimates for the Ricci-harmonic flow

In this paper we give an explicit bound of $Δ_{g(t)}u(t)$ and the local curvature estimates for the Ricci-harmonic flow under the condition that the Ricci curvature is bounded along the flow. In the second part these local curvature estimates are extended to a class of generalized Ricci flow, introduced by the author \cite{LY1}, whose stable points give Ricci-flat metrics on a complete manifold, and which is very close to the $(K, N)$-super Ricci flow recently defined by Xiangdong Li and Songzi Li \cite{LL2014}. Next we propose a conjecture for Einstein's scalar field equations motivated by a result in the first part and the bounded $L^{2}$-curvature conjecture recently solved by Klainerman, Rodnianski and Szeftel \cite{KRS2015}. In the last two parts of this paper, we discuss two notions of "Riemann curvature tensor" in the sense of Wylie-Yeroshkin \cite{KW2017, KWY2017, Wylie2015, WY2016}, respectively, and Li \cite{LY3}, whose "Ricci curvature" both give the standard Bakey-Émery Ricci curvature \cite{BE1985}, and the forward and backward uniqueness for the Ricci-harmonic flow.

math.DG↗

arXiv2018

Testing Matrix Rank, Optimally

We show that for the problem of testing if a matrix $A \in F^{n \times n}$ has rank at most $d$, or requires changing an $ε$-fraction of entries to have rank at most $d$, there is a non-adaptive query algorithm making $\widetilde{O}(d^2/ε)$ queries. Our algorithm works for any field $F$. This improves upon the previous $O(d^2/ε^2)$ bound (SODA'03), and bypasses an $Ω(d^2/ε^2)$ lower bound of (KDD'14) which holds if the algorithm is required to read a submatrix. Our algorithm is the first such algorithm which does not read a submatrix, and instead reads a carefully selected non-adaptive pattern of entries in rows and columns of $A$. We complement our algorithm with a matching query complexity lower bound for non-adaptive testers over any field. We also give tight bounds of $\widetildeΘ(d^2)$ queries in the sensing model for which query access comes in the form of $\langle X_i, A\rangle:=tr(X_i^\top A)$; perhaps surprisingly these bounds do not depend on $ε$. We next develop a novel property testing framework for testing numerical properties of a real-valued matrix $A$ more generally, which includes the stable rank, Schatten-$p$ norms, and SVD entropy. Specifically, we propose a bounded entry model, where $A$ is required to have entries bounded by $1$ in absolute value. We give upper and lower bounds for a wide range of problems in this model, and discuss connections to the sensing model above.

cs.DS↗

arXiv2018

A new embedded variable stepsize, variable order family of low computational complexity

Variable Stepsize Variable Order (VSVO) methods are the methods of choice to efficiently solve a wide range of ODEs with minimal work and assured accuracy. However, VSVO methods have limited impact in timestepping methods in complex applications due to their computational complexity and the difficulty to implement them in legacy code. We introduce a family of implicit, embedded, VSVO methods that require only one BDF solve at each time step followed by adding linear combinations of the solution at previous time levels. In particular, we construct implicit and linearly implicit VSVO methods of orders two, three and four with the same computational complexity as variable stepsize BDF3. The choice of changing the order of the method is simple and does not require additional solves of linear or nonlinear systems.

math.NA↗

arXiv2018

Learning-Based Delay-Aware Caching in Wireless D2D Caching Networks

Recently, wireless caching techniques have been studied to satisfy lower delay requirements and offload traffic from peak periods. By storing parts of the popular files at the mobile users, users can locate some of their requested files in their own caches or the caches at their neighbors. In the latter case, when a user receives files from its neighbors, device-to-device(D2D) communication is performed. D2D communication underlaid with cellular networks is also a new paradigm for the upcoming wireless systems. By allowing a pair of adjacent D2D users to communicate directly, D2D communication can achieve higher throughput, better energy efficiency and lower traffic delay. In this work, we propose an efficient learning-based caching algorithm operating together with a non-parametric estimator to minimize the average transmission delay in D2D-enabled cellular networks. It is assumed that the system does not have any prior information regarding the popularity of the files, and the non-parametric estimator is aimed at learning the intensity function of the file requests. An algorithm is devised to determine the best pairs that provide the best delay improvement in each loop to form a caching policy with very low transmission delay and high throughput. This algorithm is also extended to address a more general scenario, in which the distributions of fading coefficients and values of system parameters potentially change over time. Via numerical results, the superiority of the proposed algorithm is verified by comparing it with a naive algorithm, in which all users simply cache their favorite files, and by comparing with a probabilistic algorithm, in which the users cache a file with a probability that is proportional to its popularity.

cs.IT↗

arXiv2018

Large Margin Neural Language Model

We propose a large margin criterion for training neural language models. Conventionally, neural language models are trained by minimizing perplexity (PPL) on grammatical sentences. However, we demonstrate that PPL may not be the best metric to optimize in some tasks, and further propose a large margin formulation. The proposed method aims to enlarge the margin between the "good" and "bad" sentences in a task-specific sense. It is trained end-to-end and can be widely applied to tasks that involve re-scoring of generated text. Compared with minimum-PPL training, our method gains up to 1.1 WER reduction for speech recognition and 1.0 BLEU increase for machine translation.

cs.CL↗

arXiv2018

Patch-based Contour Prior Image Denoising for Salt and Pepper Noise

The salt and pepper noise brings a significant challenge to image denoising technology, i.e. how to removal the noise clearly and retain the details effectively? In this paper, we propose a patch-based contour prior denoising approach for salt and pepper noise. First, noisy image is cut into patches as basic representation unit, a discrete total variation model is designed to extract contour structures; Second, a weighted Euclidean distance is designed to search the most similar patches, then, corresponding contour stencils are extracted from these similar patches; At the last, we build filter from contour stencils in the framework of regression. Numerical results illustrate that the proposed method is competitive with the state-of-the-art methods in terms of the peak signal-to-noise (PSNR) and visual effects.

cs.MM↗

arXiv2018

A Convolutional Neural Networks Denoising Approach for Salt and Pepper Noise

The salt and pepper noise, especially the one with extremely high percentage of impulses, brings a significant challenge to image denoising. In this paper, we propose a non-local switching filter convolutional neural network denoising algorithm, named NLSF-CNN, for salt and pepper noise. As its name suggested, our NLSF-CNN consists of two steps, i.e., a NLSF processing step and a CNN training step. First, we develop a NLSF pre-processing step for noisy images using non-local information. Then, the pre-processed images are divided into patches and used for CNN training, leading to a CNN denoising model for future noisy images. We conduct a number of experiments to evaluate the effectiveness of NLSF-CNN. Experimental results show that NLSF-CNN outperforms the state-of-the-art denoising algorithms with a few training images.

cs.MM↗

arXiv2018

Optimizing hot electron harvesting at planar metal-semiconductor interfaces with titanium oxynitride thin films

Understanding metal-semiconductor interfaces is critical to the advancement of photocatalysis and sub-bandgap solar energy harvesting where sub-bandgap photons can be excited and extracted into the semiconductor. In this work, we compare the electron extraction efficiency across Au/TiO2 and titanium oxynitride/TiO2-x interfaces, where in the latter case the spontaneously forming oxide layer (TiO2-x) creates a metal-semiconductor contact. Time-resolved pump-probe spectroscopy is used to study the electron recombination rates in both cases. Unlike the nanosecond recombination lifetimes in Au/TiO2, we find a bottleneck in the electron relaxation in the TiON system, which we explain using a trap-mediated recombination model. Using this model, we investigate the tunability of the relaxation dynamics with oxygen content in the parent film. The optimized film (TiO0.5N0.5) exhibits the highest carrier extraction efficiency, slowest trapping and an appreciable hot electron population reaching the surface oxide. Our results demonstrate the productive role oxygen can play in enhancing electron harvesting and elongating electron lifetimes providing an optimized metal-semiconductor interface using only the native oxide of titanium oxynitride.

cond-mat.mes-hall↗

arXiv2018

Identifying viruses from metagenomic data by deep learning

The recent development of metagenomic sequencing makes it possible to sequence microbial genomes including viruses in an environmental sample. Identifying viral sequences from metagenomic data is critical for downstream virus analyses. The existing reference-based and gene homology-based methods are not efficient in identifying unknown viruses or short viral sequences. Here we have developed a reference-free and alignment-free machine learning method, DeepVirFinder, for predicting viral sequences in metagenomic data using deep learning techniques. DeepVirFinder was trained based on a large number of viral sequences discovered before May 2015. Evaluated on the sequences after that date, DeepVirFinder outperformed the state-of-the-art method VirFinder at all contig lengths. Enlarging the training data by adding millions of purified viral sequences from environmental metavirome samples significantly improves the accuracy for predicting under-represented viruses. Applying DeepVirFinder to real human gut metagenomic samples from patients with colorectal carcinoma (CRC) identified 51,138 viral sequences belonging to 175 bins. Ten bins were associated with the cancer status, indicating their potential use for non-invasive diagnosis of CRC. In summary, DeepVirFinder greatly improved the precision and recall rates of viral identification, and it will significantly accelerate the discovery rate of viruses.

q-bio.GN↗

arXiv2018

All-loop Mondrian Diagrammatics and 4-particle Amplituhedron

Based on 1712.09990 which handles the 4-particle amplituhedron at 3-loop, we have found an extremely simple pattern, yet far more non-trivial than one might naturally expect: the all-loop Mondrian diagrammatics. By further simplifying and rephrasing the key relation of positivity in the amplituhedron setting, remarkably, we find a completeness relation unifying all diagrams of the Mondrian types for the 4-particle integrand of planar N=4 SYM to all loop orders, each of which can be mapped to a simple product following a few plain rules designed for this relation. The explicit examples we investigate span from 3-loop to 7-loop order, and based on them, we classify the basic patterns of Mondrian diagrams into four types: the ladder, cross, brick-wall and spiral patterns. Interestingly, for some special combinations of ordered subspaces (a concept defined in the previous work), we find failed exceptions of the completeness relation which are called "anomalies", nevertheless, they substantially give hints on the all-loop recursive proof of this relation. These investigations are closely related to the combinatoric knowledge of separable permutations and Schroeder numbers, and go even further from a diagrammatic perspective. For physical relevance, we need to further consider dual conformal invariance for two basic diagrammatic patterns to correct the numerator for a local integrand involving one or both of such patterns, while the denominator encoding its pole structure and also the sign factor, are already fixed by rules of the completeness relation. With this extra treatment to ensure the integrals are dual conformally invariant, each Mondrian diagram can be exactly translated to its corresponding physical loop integrand after being summed over all ordered subspaces that admit it.

hep-th↗

arXiv2018

Cancer Metastasis Detection With Neural Conditional Random Field

Breast cancer diagnosis often requires accurate detection of metastasis in lymph nodes through Whole-slide Images (WSIs). Recent advances in deep convolutional neural networks (CNNs) have shown significant successes in medical image analysis and particularly in computational histopathology. Because of the outrageous large size of WSIs, most of the methods divide one slide into lots of small image patches and perform classification on each patch independently. However, neighboring patches often share spatial correlations, and ignoring these spatial correlations may result in inconsistent predictions. In this paper, we propose a neural conditional random field (NCRF) deep learning framework to detect cancer metastasis in WSIs. NCRF considers the spatial correlations between neighboring patches through a fully connected CRF which is directly incorporated on top of a CNN feature extractor. The whole deep network can be trained end-to-end with standard back-propagation algorithm with minor computational overhead from the CRF component. The CNN feature extractor can also benefit from considering spatial correlations via the CRF component. Compared to the baseline method without considering spatial correlations, we show that the proposed NCRF framework obtains probability maps of patch predictions with better visual quality. We also demonstrate that our method outperforms the baseline in cancer metastasis detection on the Camelyon16 dataset and achieves an average FROC score of 0.8096 on the test set. NCRF is open sourced at https://github.com/baidu-research/NCRF.

cs.CV↗

arXiv2018

Verifying Probabilistic Timed Automata Against Omega-Regular Dense-Time Properties

Probabilistic timed automata (PTAs) are timed automata (TAs) extended with discrete probability distributions.They serve as a mathematical model for a wide range of applications that involve both stochastic and timed behaviours. In this work, we consider the problem of model-checking linear \emph{dense-time} properties over {PTAs}. In particular, we study linear dense-time properties that can be encoded by TAs with infinite acceptance criterion.First, we show that the problem of model-checking PTAs against deterministic-TA specifications can be solved through a product construction. Based on the product construction, we prove that the computational complexity of the problem with deterministic-TA specifications is EXPTIME-complete. Then we show that when relaxed to general (nondeterministic) TAs, the model-checking problem becomes undecidable.Our results substantially extend state of the art with both the dense-time feature and the nondeterminism in TAs.

cs.FL↗

arXiv2018

Deterministic Heavy Hitters with Sublinear Query Time

This paper studies the classic problem of finding heavy hitters in the turnstile streaming model. We give the first deterministic linear sketch that has $O(ε^{-2} \log n \cdot \log^*(ε^{-1}))$ rows and answers queries in sublinear time. The number of rows is only a factor of $\log^*(ε^{-1})$ more than that used by the state-of-the-art algorithm prior to our paper due to Nelson, Nguyen and Woodruff (RANDOM'12). Their algorithm runs in time at least linear in the universe size $n$, which is highly undesirable in streaming applications. Our approach is based on an iterative procedure, where most unrecovered heavy hitters are identified in each iteration. Although this technique has been extensively employed in the related problem of sparse recovery, this is the first time, to the best of our knowledge, that it has been used in the context of $\ell_1$ heavy hitters. Along the way, we also give sublinear time algorithms for the closely related problems of combinatorial group testing and $\ell_1/\ell_1$ compressed sensing, matching the space usage of previous (super-)linear time algorithms.

cs.DS↗

arXiv2018

Local curvature estimates for the Laplacian flow

In this paper we give local curvature estimates for the Laplacian flow on closed G_2-structures under the condition that the Ricci curvature is bounded along the flow. The main ingredient consists of the idea of Kotschwar-Munteanu-Wang who gave local curvature estimates for the Ricci flow on complete manifolds and then provided a new elementary proof of Sesum's result, and the particular structure of the Laplacian flow on closed G_2-structures. As an immediate consequence, this estimates give a new proof of Lotay-Wei's result which is an analogue of Sesum's theorem. The second result is about an interesting evolution equation for the scalar curvature of the Laplacian flow of closed G_2-structures. Roughly speaking, we can prove that the time derivative of the scalar curvature R_t is equal to the Laplacian of R_t, plus an extra term which can be written as the difference of two nonnegative quantities.

math.DG↗

arXiv2018

Covariance-Insured Screening

Modern bio-technologies have produced a vast amount of high-throughput data with the number of predictors far greater than the sample size. In order to identify more novel biomarkers and understand biological mechanisms, it is vital to detect signals weakly associated with outcomes among ultrahigh-dimensional predictors. However, existing screening methods, which typically ignore correlation information, are likely to miss these weak signals. By incorporating the inter-feature dependence, we propose a covariance-insured screening methodology to identify predictors that are jointly informative but only marginally weakly associated with outcomes. The validity of the method is examined via extensive simulations and real data studies for selecting potential genetic factors related to the onset of cancer.

stat.ML↗

arXiv2018

Stability of the Nagaoka-type Ferromagnetic State in a $t_{2g}$ Orbital System on a Cubic Lattice

We generalize the previous exact results of the Nagaoka-type itinerant ferromagnetic states in a three dimensional $t_{2g}$-orbital system to allow for multiple holes. The system is a simple cubic lattice with each site possessing $d_{xy}$, $d_{yz}$, and $d_{xz}$ orbitals, which allow two-dimensional hopping within each orbital plane. In the strong coupling limit of $U\to \infty$, the orbital-generalized Nagaoka ferromagnetic states are proved degenerate with the ground state in the thermodynamic limit when the hole number per orbital layer scales slower than $L^{\frac{1}{2}}$. This result is valid for arbitrary values of the ferromagnetic Hund's coupling $J>0$ and inter-orbital repulsion $V\ge 0$. The stability of the Nagaoka-type state at finite electron densities with respect to a single spin-flip is investigated. These results provide helpful guidance for studying the mechanism of itinerant ferromagnetism for the $t_{2g}$-orbital materials.

cond-mat.str-el↗

arXiv2018

Exact Results on Itinerant Ferromagnetism and the 15-puzzle Problem

We apply a result from graph theory to prove exact results about itinerant ferromagnetism. Nagaoka's theorem of ferromagnetism is extended to all non-separable graphs except single polygons with more than four vertices by applying the solution to the generalized 15-puzzle problem, which studies whether the hole's motion can connect all possible tile configurations. This proves that the ground state of a $U\to\infty$ Hubbard model with one hole away from the half filling on a 2D honeycomb lattice or a 3D diamond lattice is fully spin-polarized. Furthermore, the condition of connectivity for $N$-component fermions is presented, and Nagaoka's theorem is also generalized to $SU(N)$-symmetric fermion systems on non-separable graphs.

cond-mat.str-el↗