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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,742 papers · 148 categories

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144288431575 · Jun 202019922001200920172026
48 results for Run-time Efficiency

Efficiently learns complex Boolean functions under Gaussian distributions.

problem Learning complex Boolean functions of halfspaces under Gaussian marginals.
method First efficient proper agnostic learning algorithm for arbitrary Boolean functions of K halfspaces.
result Matches the best known improper learning algorithm's run-time dependence on dimension.

This paper develops coding techniques to reduce the running time of distributed learning tasks. It characterizes the fundamental tradeoff to compute gradients (and more generally vector summations) in terms of three parameters: computation load, straggler tolerance and communication cost. It further gives an explicit c…

2018-02-09abs ↗pdf ↗

Recurrent neural networks can be large and compute-intensive, yet many applications that benefit from RNNs run on small devices with very limited compute and storage capabilities while still having run-time constraints. As a result, there is a need for compression techniques that can achieve significant compression wit…

2019-06-12abs ↗pdf ↗

In this paper, we consider efficient differentially private empirical risk minimization from the viewpoint of optimization algorithms. For strongly convex and smooth objectives, we prove that gradient descent with output perturbation not only achieves nearly optimal utility, but also significantly improves the running …

2017-03-29abs ↗pdf ↗

We describe two techniques that significantly improve the running time of several standard machine-learning algorithms when data is sparse. The first technique is an algorithm that effeciently extracts one-way and two-way counts--either real or expected-- from discrete data. Extracting such counts is a fundamental step…

2013-01-23abs ↗pdf ↗

We introduce dropout compaction, a novel method for training feed-forward neural networks which realizes the performance gains of training a large model with dropout regularization, yet extracts a compact neural network for run-time efficiency. In the proposed method, we introduce a sparsity-inducing prior on the per u…

2016-11-18abs ↗pdf ↗

We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise -- where an ε\varepsilon-fraction of our samples were chosen by an adversary. We give robust estimators that achieve estimation error O(ε)O(\varepsilon) in the total variation distance, which is optimal up…

2017-04-12abs ↗pdf ↗

While matrix factorisation models are ubiquitous in large scale recommendation and search, real time application of such models requires inner product computations over an intractably large set of item factors. In this manuscript we present a novel framework that uses the inverted index representation to exploit struct…

2016-05-16abs ↗pdf ↗

New framework reduces private mean estimation error with optimal efficiency.

problem Locally private mean estimation of high-dimensional vectors.
method ProjUnit framework: random projections, normalization, and optimal algorithm execution in lower dimensions.
result Optimal error up to a 1+o(1)-factor with computational efficiency and low communication complexity.

This article introduces the concepts around Online Bandit Linear Optimization and explores an efficient setup called SCRiBLe (Self-Concordant Regularization in Bandit Learning) created by Abernethy et. al.\cite{abernethy}. The SCRiBLe setup and algorithm yield a O(T)O(\sqrt{T}) regret bound and polynomial run time comple…

2018-05-11abs ↗pdf ↗

We propose a novel and flexible rank-breaking-then-composite-marginal-likelihood (RBCML) framework for learning random utility models (RUMs), which include the Plackett-Luce model. We characterize conditions for the objective function of RBCML to be strictly log-concave by proving that strict log-concavity is preserved…

2018-06-04abs ↗pdf ↗

We study kk-GenEV, the problem of finding the top kk generalized eigenvectors, and kk-CCA, the problem of finding the top kk vectors in canonical-correlation analysis. We propose algorithms LazyEV\mathtt{LazyEV} and LazyCCA\mathtt{LazyCCA} to solve the two problems with running times linearly dependent on the input size and…

2016-07-20abs ↗pdf ↗

Efficient algorithms improve learning of large-margin halfspaces.

problem Learning large-margin halfspaces efficiently and reproducibly.
method Design of efficient, dimension-independent, polynomial-time algorithms; SGD-based approach; DP-to-Replicability reduction.
result Improved sample complexity compared to previous algorithms, with optimal sample complexity for one algorithm.

Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this paper, we present an inexact augmented Lagrangian method to solve the Lasso problem …

2019-03-12abs ↗pdf ↗

We prove that stochastic gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy observations generated by the system. Even though the objective function is non-convex, we provide polynomial running …

2016-09-16abs ↗pdf ↗

We develop an efficient algorithm for low-rank approximation with improved approximation guarantees.

problem Optimal low-rank approximation of matrices with 1\ell_1 norm constraints.
method Polynomial time column subset selection-based algorithm achieving ildeO(k1/2) ilde{O}(k^{1/2})-approximation.
result Improved approximation guarantees for 1\ell_1 low-rank approximation.

We address the problem of learning in an online setting where the learner repeatedly observes features, selects among a set of actions, and receives reward for the action taken. We provide the first efficient algorithm with an optimal regret. Our algorithm uses a cost sensitive classification learner as an oracle and h…

2011-06-13abs ↗pdf ↗

The paper proposes using function approximations to reduce the computational burden in measuring counterparty credit exposure.

problem The need for regular exposure calculations in finance, balancing between computational cost and risk simplification.
method Replacing derivative pricers with function approximations, proving error bounds, and using Chebyshev interpolation for convergence.
result Derives probabilistic and finite sample error bounds, showing significant run-time reductions and asymptotic efficiency gains.

New algorithm estimates Gaussian means and covariances efficiently and privately.

problem Estimating Gaussian parameters privately and efficiently.
method Differentially private preconditioner to transform arbitrary Gaussian samples.
result First polynomial-time, sample-efficient estimator for arbitrary Gaussian distributions.

Non-linear kernel methods can be approximated by fast linear ones using suitable explicit feature maps allowing their application to large scale problems. We investigate how convolution kernels for structured data are composed from base kernels and construct corresponding feature maps. On this basis we propose exact an…

2017-03-02abs ↗pdf ↗

Belief propagation and its variants are popular methods for approximate inference, but their running time and even their convergence depend greatly on the schedule used to send the messages. Recently, dynamic update schedules have been shown to converge much faster on hard networks than static schedules, namely the res…

2012-06-20abs ↗pdf ↗

Long short-term memory (LSTM) has been widely used for sequential data modeling. Researchers have increased LSTM depth by stacking LSTM cells to improve performance. This incurs model redundancy, increases run-time delay, and makes the LSTMs more prone to overfitting. To address these problems, we propose a hidden-laye…

2018-05-30abs ↗pdf ↗

Unified approach for robust and heavy-tailed mean estimation in high dimensions.

problem Estimating mean in high dimensions with adversarial corruption or heavy-tailed distributions.
method Unified meta-problem and duality theorem leading to Filter algorithm and QUE scheme.
result Unified and efficient algorithms for both robust and heavy-tailed mean estimation.

Efficient method for learning continuous exponential families beyond Gaussian.

problem Learning continuous exponential families with unbounded support.
method Interaction Screening approach for scalable learning of continuous graphical models.
result Our estimator maintains similar accuracy and sample complexity scalings compared to alternative approaches, while improving run-time.

Significant progress has been made in the area of model-based reinforcement learning. State-of-the-art algorithms are now able to match the asymptotic performance of model-free methods while being significantly more data efficient. However, this success has come at a price: state-of-the-art model-based methods require …

2019-10-28abs ↗pdf ↗

Randomly chosen support makes sparse linear regression easy.

problem Sparse linear regression with random support.
method Random support selection for efficient prediction.
result Prediction error εε with N=extpoly(k,logd,1/ε)N = ext{poly}(k, \log d, 1/ε) samples and extpoly(d,N) ext{poly}(d,N) run-time.

The colored Jones polynomial is a knot invariant that plays a central role in low dimensional topology. We give a simple and an efficient algorithm to compute the colored Jones polynomial of any knot. Our algorithm utilizes the walks along a braid model of the colored Jones polynomial that was refined by Armond from th…

2018-04-21abs ↗pdf ↗

The kernel method is a potential approach to analyzing structured data such as sequences, trees, and graphs; however, unordered trees have not been investigated extensively. Kimura et al. (2011) proposed a kernel function for unordered trees on the basis of their subpaths, which are vertical substructures of trees resp…

2012-06-18abs ↗pdf ↗