亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

Stochastic variance reduction has proven effective at accelerating first-order algorithms for solving convex finite-sum optimization tasks such as empirical risk minimization. Incorporating additional second-order information has proven helpful in further improving the performance of these first-order methods. However, comparatively little is known about the benefits of using variance reduction to accelerate popular stochastic second-order methods such as Subsampled Newton. To address this, we propose Stochastic Variance-Reduced Newton (SVRN), a finite-sum minimization algorithm which enjoys all the benefits of second-order methods: simple unit step size, easily parallelizable large-batch operations, and fast local convergence, while at the same time taking advantage of variance reduction to achieve improved convergence rates (per data pass) for smooth and strongly convex problems. We show that SVRN can accelerate many stochastic second-order methods (such as Subsampled Newton) as well as iterative least squares solvers (such as Iterative Hessian Sketch), and it compares favorably to popular first-order methods with variance reduction.

Batch normalization (BN) has become a critical component across diverse deep neural networks. The network with BN is invariant to positively linear re-scale transformation, which makes there exist infinite functionally equivalent networks with different scales of weights. However, optimizing these equivalent networks with the first-order method such as stochastic gradient descent will obtain a series of iterates converging to different local optima owing to their different gradients across training. To obviate this, we propose a quotient manifold \emph{PSI manifold}, in which all the equivalent weights of the network with BN are regarded as the same element. Next, we construct gradient descent and stochastic gradient descent on the proposed PSI manifold to train the network with BN. The two algorithms guarantee that every group of equivalent weights (caused by positively re-scaling) converge to the equivalent optima. Besides that, we give convergence rates of the proposed algorithms on the PSI manifold. The results show that our methods accelerate training compared with the algorithms on the Euclidean weight space. Finally, empirical results verify that our algorithms consistently improve the existing methods in both convergence rate and generalization ability under various experimental settings.

A method to perform offline and online speaker diarization for an unlimited number of speakers is described in this paper. End-to-end neural diarization (EEND) has achieved overlap-aware speaker diarization by formulating it as a multi-label classification problem. It has also been extended for a flexible number of speakers by introducing speaker-wise attractors. However, the output number of speakers of attractor-based EEND is empirically capped; it cannot deal with cases where the number of speakers appearing during inference is higher than that during training because its speaker counting is trained in a fully supervised manner. Our method, EEND-GLA, solves this problem by introducing unsupervised clustering into attractor-based EEND. In the method, the input audio is first divided into short blocks, then attractor-based diarization is performed for each block, and finally the results of each blocks are clustered on the basis of the similarity between locally-calculated attractors. While the number of output speakers is limited within each block, the total number of speakers estimated for the entire input can be higher than the limitation. To use EEND-GLA in an online manner, our method also extends the speaker-tracing buffer, which was originally proposed to enable online inference of conventional EEND. We introduces a block-wise buffer update to make the speaker-tracing buffer compatible with EEND-GLA. Finally, to improve online diarization, our method improves the buffer update method and revisits the variable chunk-size training of EEND. The experimental results demonstrate that EEND-GLA can perform speaker diarization of an unseen number of speakers in both offline and online inferences.

In this paper, we study the trace regression when a matrix of parameters B* is estimated via convex relaxation of a rank-penalized regression or via non-convex optimization. It is known that these estimators satisfy near-optimal error bounds under assumptions on rank, coherence, or spikiness of B*. We start by introducing a general notion of spikiness for B* that provides a generic recipe to prove restricted strong convexity for the sampling operator of the trace regression and obtain near-optimal and non-asymptotic error bounds for the estimation error. Similar to the existing literature, these results require the penalty parameter to be above a certain theory-inspired threshold that depends on the observation noise and the sampling operator which may be unknown in practice. Next, we extend the error bounds to the cases when the regularization parameter is chosen via cross-validation. This result is significant in that existing theoretical results on cross-validated estimators do not apply to our setting since the estimators we study are not known to satisfy their required notion of stability. Finally, using simulations on synthetic and real data, we show that the cross-validated estimator selects a nearly-optimal penalty parameter and outperforms the theory-inspired approach of selecting the parameter.

We consider the problem of secure distributed matrix multiplication (SDMM), where a user has two matrices and wishes to compute their product with the help of $N$ honest but curious servers under the security constraint that any information about either $A$ or $B$ is not leaked to any server. This paper presents a \emph{new scheme} that considers a grid product partition for matrices $A$ and $B$, which achieves an upload cost significantly lower than the existing results in the literature. Since the grid partition is a general partition that incorporates the inner and outer ones, it turns out that the communication load of the proposed scheme matches the best-known protocols for those extreme cases.

Non-negative Matrix Factorization (NMF) is an intensively used technique for obtaining parts-based, lower dimensional and non-negative representation of non-negative data. It is a popular method in different research fields. Scientists performing research in the fields of biology, medicine and pharmacy often prefer NMF over other dimensionality reduction approaches (such as PCA) because the non-negativity of the approach naturally fits the characteristics of the domain problem and its result is easier to analyze and understand. Despite these advantages, it still can be hard to get exact characterization and interpretation of the NMF's resulting latent factors due to their numerical nature. On the other hand, rule-based approaches are often considered more interpretable but lack the parts-based interpretation. In this work, we present a version of the NMF approach that merges rule-based descriptions with advantages of part-based representation offered by the NMF approach. Given the numerical input data with non-negative entries and a set of rules with high entity coverage, the approach creates the lower-dimensional non-negative representation of the input data in such a way that its factors are described by the appropriate subset of the input rules. In addition to revealing important attributes for latent factors, it allows analyzing relations between these attributes and provides the exact numerical intervals or categorical values they take. The proposed approach provides numerous advantages in tasks such as focused embedding or performing supervised multi-label NMF.

Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is sub-optimal when the sample size is comparable to or less than the number of features. Such high-dimensional settings are common in modern genomics, where covariance matrix estimation is frequently employed as a method for inferring gene networks. To achieve estimation accuracy in these settings, existing methods typically either assume that the population covariance matrix has some particular structure, for example sparsity, or apply shrinkage to better estimate the population eigenvalues. In this paper, we study a new approach to estimating high-dimensional covariance matrices. We first frame covariance matrix estimation as a compound decision problem. This motivates defining a class of decision rules and using a nonparametric empirical Bayes g-modeling approach to estimate the optimal rule in the class. Simulation results and gene network inference in an RNA-seq experiment in mouse show that our approach is comparable to or can outperform a number of state-of-the-art proposals.

A method for practical realization of the inverse scattering transform method for the Korteweg-de Vries equation is proposed. It is based on analytical representations for Jost solutions and for integral kernels of transformation operators obtained recently by the authors. The representations have the form of functional series in which the first coefficient plays a crucial role both in solving the direct scattering and the inverse scattering problems. The direct scattering problem reduces to computation of a number of the coefficients following a simple recurrent integration procedure with a posterior calculation of scattering data by well known formulas. The inverse scattering problem reduces to a system of linear algebraic equations from which the first component of the solution vector leads to the recovery of the potential. We prove the applicability of the finite section method to the system of linear algebraic equations and discuss numerical aspects of the proposed method. Numerical examples are given, which reveal the accuracy and speed of the method.

A striking observation about iterative magnitude pruning (IMP; Frankle et al. 2020) is that $\unicode{x2014}$ after just a few hundred steps of dense training $\unicode{x2014}$ the method can find a sparse sub-network that can be trained to the same accuracy as the dense network. However, the same does not hold at step 0, i.e. random initialization. In this work, we seek to understand how this early phase of pre-training leads to a good initialization for IMP both through the lens of the data distribution and the loss landscape geometry. Empirically we observe that, holding the number of pre-training iterations constant, training on a small fraction of (randomly chosen) data suffices to obtain an equally good initialization for IMP. We additionally observe that by pre-training only on "easy" training data, we can decrease the number of steps necessary to find a good initialization for IMP compared to training on the full dataset or a randomly chosen subset. Finally, we identify novel properties of the loss landscape of dense networks that are predictive of IMP performance, showing in particular that more examples being linearly mode connected in the dense network correlates well with good initializations for IMP. Combined, these results provide new insight into the role played by the early phase training in IMP.

Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization algorithms due to their susceptibility to spurious local minima, simple iterative methods such as gradient descent have been remarkably successful in practice. The theoretical footings, however, had been largely lacking until recently. In this tutorial-style overview, we highlight the important role of statistical models in enabling efficient nonconvex optimization with performance guarantees. We review two contrasting approaches: (1) two-stage algorithms, which consist of a tailored initialization step followed by successive refinement; and (2) global landscape analysis and initialization-free algorithms. Several canonical matrix factorization problems are discussed, including but not limited to matrix sensing, phase retrieval, matrix completion, blind deconvolution, robust principal component analysis, phase synchronization, and joint alignment. Special care is taken to illustrate the key technical insights underlying their analyses. This article serves as a testament that the integrated consideration of optimization and statistics leads to fruitful research findings.