This paper considers the sparse eigenvalue problem, which is to extract dominant (largest) sparse eigenvectors with at most non-zero components. We propose a simple yet effective solution called truncated power method that can approximately solve the underlying nonconvex optimization problem. A strong sparse recove…
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48 results for “Truncated Power Method”
Truncated densities are probability density functions defined on truncated domains. They share the same parametric form with their non-truncated counterparts up to a normalizing constant. Since the computation of their normalizing constants is usually infeasible, Maximum Likelihood Estimation cannot be easily applied t…
Systems with Correlations in the Variance: Generating Power-Law Tails in Probability Distributionscond-mat.stat-mech
We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated Lévy distribution. For both (i) and (ii), we find that due to the correlations in the variance,…
Choppy optimizes ranked list truncation using Transformer architecture.
problem Optimal truncation of ranked search results to balance relevance and user cost.
method Assumption-free Transformer model optimizing user-defined IR metrics.
result Choppy improves upon recent state-of-the-art methods.
New method improves DAG learning by using large coefficients for higher-order terms.
problem Recovering DAG structures from observational data is challenging due to combinatorial optimization.
method Proposes truncated matrix power iteration to approximate DAG constraints efficiently.
result Empirically outperforms previous methods by a factor of 3 or more in structural Hamming distance.
Gradually Truncated Log-normal distribution - Size distribution of firmscond-mat.stat-mech
Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with step size compared to normal distribution. Thus it is essential to cut-off these di…
We give a microscopic representation of the stock-market in which the microscopic agents are the individual traders and their capital. Their basic dynamics consists in the auto-catalysis of the individual capital and in the global competition/cooperation between the agents mediated by the total wealth invested in the s…
We propose a novel sparse tensor decomposition method, namely Tensor Truncated Power (TTP) method, that incorporates variable selection into the estimation of decomposition components. The sparsity is achieved via an efficient truncation step embedded in the tensor power iteration. Our method applies to a broad family …
We propose a new framework for Hamiltonian Monte Carlo (HMC) on truncated probability distributions with smooth underlying density functions. Traditional HMC requires computing the gradient of potential function associated with the target distribution, and therefore does not perform its full power on truncated distribu…
We study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws in the size distribution of their individual elements. The exponents of the…
We accelerate CNF by reducing ODE truncation errors with polynomial regularization.
problem High computation cost of CNF due to large truncation errors in solving ODEs.
method Add polynomial regularization to approximate ODE trajectories with polynomial functions.
result 42.3% to 71.3% reduction of NFE on density estimation, 19.3% to 32.1% on variational auto-encoder.
The problem of an arbitrary truncated Levy flight description using the method of cumulant approach has been solved. The set of cumulants of the truncated Levy distribution given the assumption of arbitrary truncation has been found. The influence of truncation shape on the truncated Levy flight properties in the Gauss…
Generalized score matching for densities on general domains.
problem Estimating density functions on complex, non-standard domains.
method A generalized score matching approach for densities on general domains.
result The method provides theoretical guarantees and empirical advantages.
New method for constructing truncated vine copulas.
problem High-dimensional parameter space in vine copulas.
method Propose a new score and algorithm for constructing truncated vines.
result New algorithms exploit conditional independences.
Compute group cohomology for mapping class group with non-symplectic coefficients.
problem Compute group cohomology for mapping class group with non-symplectic coefficients.
method Compute the invariant subspace of the rational group ring of a surface, truncated by powers of the augmentation ideal, under the action of the mapping class group.
result First group cohomology computation for the mapping class group with non-symplectic coefficients.
New combinatorial method for sparse PCA works beyond spiked identity model.
problem Sparse PCA under general covariance matrices.
method Combinatorial truncated power method with global convergence guarantee.
result First combinatorial sparse PCA method provably successful for general covariance matrices.
In the past years, Deep convolution neural network has achieved great success in many artificial intelligence applications. However, its enormous model size and massive computation cost have become the main obstacle for deployment of such powerful algorithm in the low power and resource-limited mobile systems. As the c…
New COS method formula improves option pricing accuracy.
problem Determining the optimal truncation range for COS method.
method Derive new formula using Markov's inequality to ensure convergence.
result New formula leads to more accurate option pricing.
Improved neural likelihood estimation for SSMs with truncated-SNL.
problem Challenges in parameter inference for state-space models.
method Truncated-SNL: a novel inference algorithm addressing SNL's limitations.
result Truncated-SNL is more accurate, scalable, and sample-efficient.
ParPIC clusters directed graphs using random walks and diffusion operators.
problem Challenges in vertex-level clustering for directed graphs due to edge directionality.
method Parametrized Power-Iteration Clustering (ParPIC) based on reversible random walks and diffusion operators.
result ParPIC achieves competitive clustering accuracy with improved scalability compared to spectral and teleportation-based methods.
Smoothing splines provide a powerful and flexible means for nonparametric estimation and inference. With a cubic time complexity, fitting smoothing spline models to large data is computationally prohibitive. In this paper, we use the theoretical optimal eigenspace to derive a low rank approximation of the smoothing spl…
Score matching method improves density estimation for truncated data on manifolds.
problem Density estimation for truncated data on manifolds with intractable normalising constant.
method Truncated score matching extended to Riemannian manifolds with boundary.
result Score matching estimator approximates true parameter values with low error.
Truncated backpropagation through time (TBPTT) is a popular method for learning in recurrent neural networks (RNNs) that saves computation and memory at the cost of bias by truncating backpropagation after a fixed number of lags. In practice, choosing the optimal truncation length is difficult: TBPTT will not converge …
The method approximates stationary distributions of Markov models by truncating irrelevant states.
problem Computing the stationary distribution of complex Markov models is computationally challenging.
method A state-space lumping scheme that aggregates states in a grid structure, iteratively refining the state-space.
result The method provides a well-justified finite-state projection tailored to the stationary behavior of Markov models.
We solve for functions from their truncated Hilbert transforms using Chebyshev series.
problem Finding functions from their truncated Hilbert transforms.
method Express functions in Chebyshev series and numerically estimate coefficients.
result Numerical methods work well for extrapolating functions from truncated Hilbert transforms.
The paper analyzes and mitigates biases in scalable Gaussian Process methods.
problem Modeling biases in scalable Gaussian Process methods.
method Randomized truncation estimators to eliminate bias in exchange for increased variance.
result Randomized truncation estimators meaningfully outperform biased counterparts with minimal additional computation.
Paper proposes a new method for PCA using generative models.
problem Principal component analysis with generative modeling assumptions.
method Quadratic estimator and power method variant.
result Near-matching statistical rate of order .
Paper proposes approximate Stein classes for efficient truncated density estimation.
problem Difficulties in estimating truncated density models due to intractable normalising constants and boundary conditions.
method Adapts score matching to solve the problem, introduces approximate Stein classes and a novel discrepancy measure, TKSD.
result TKSD does not require a fixed weighting function and can be evaluated using only boundary samples, leading to improved accuracy.
A new kernel test reduces noise in MMD by focusing on leading eigen-directions.
problem Noise in trailing directional components degrades power of standard kernel two-sample tests.
method Truncate MMD spectral decomposition, retaining only leading eigen-directions.
result Our method achieves superior power and robustness, especially in high-dimensional and unbalanced settings.
Controlling Overestimation Bias with Truncated Mixture of Continuous Distributional Quantile Criticscs.LG
Paper tackles overestimation bias in continuous control, improving performance by 25%.
problem Overestimation bias in off-policy learning.
method Truncated Quantile Critics (TQC) combines distributional representation, truncation, and ensembling of critics.
result TQC outperforms state-of-the-art methods by 25% on the Humanoid environment.
Sparse PCA is a widely used technique for high-dimensional data analysis. In this paper, we propose a new method called low-rank principal eigenmatrix analysis. Different from sparse PCA, the dominant eigenvectors are allowed to be dense but are assumed to have a low-rank structure when matricized appropriately. Such a…
In this paper, we develop a general theory of truncated inverse binomial sampling. In this theory, the fixed-size sampling and inverse binomial sampling are accommodated as special cases. In particular, the classical Chernoff-Hoeffding bound is an immediate consequence of the theory. Moreover, we propose a rigorous and…
ALTBI: Constructing Improved Outlier Detection Models via Optimization of Inlier-Memorization Effectstat.ML
ALTBI enhances outlier detection by maximizing the inlier-memorization effect.
problem Improving outlier detection models via optimization of inlier-memorization effect.
method ALTBI introduces two techniques: increasing mini-batch size and using adaptive threshold for truncated loss function.
result ALTBI achieves state-of-the-art performance in identifying outliers with lower computation costs.
Learning with a {\it convex loss} function has been a dominating paradigm for many years. It remains an interesting question how non-convex loss functions help improve the generalization of learning with broad applicability. In this paper, we study a family of objective functions formed by truncating traditional loss f…
Estimates domain truncation error for option pricing PDEs.
problem Estimating error in option pricing models with domain truncation.
method Derives an estimate of domain truncation error for a multidimensional PDE system.
result Proposes a sharper error estimate for option pricing models.
Improved wind speed forecasts for power generation using machine learning.
problem Improving the accuracy and reliability of wind speed predictions for power generation.
method A novel machine learning approach for calibrating wind speed ensemble forecasts.
result The proposed method improves the calibration and accuracy of probabilistic and point forecasts.
A new method for multi-objective Bayesian optimization using entropy search and variational lower bound maximization.
problem Efficiently optimizing multiple objectives in continuous domains.
method Approximates the Pareto-frontier using a mixture distribution and optimizes the balance through variational lower bound maximization.
result Demonstrated effectiveness especially with many objective functions.
A new method optimizes diffusion models with recursive likelihood ratios.
problem Efficiently aligning pre-trained diffusion models for specific applications.
method Recursive Likelihood Ratio (RLR) optimizer for Half-Order (HO) fine-tuning.
result The RLR method achieves unbiased and lower-variance gradients, improving model performance.
Efficiently estimate Boolean product distribution parameters from truncated samples.
problem Estimating parameters of Boolean product distributions from truncated samples.
method Introducing fatness of truncation set, using membership queries, and adapting Stochastic Gradient Descent.
result Efficiently learn Boolean product distributions from truncated samples with small sample complexity.
In the paper "On Truncated Variation of Brownian Motion with Drift" (Bull. Pol. Acad. Sci. Math. 56 (2008), no.4, 267 - 281) we defined truncated variation of Brownian motion with drift, where is a standard Brownian motion. Truncated variation differs from regular variation by neglect…
Fast algorithms for learning a Gaussian under halfspace truncation with optimal sample complexitycs.DS
Optimal algorithm learns Gaussian under halfspace truncation with minimal samples.
problem Learning a Gaussian distribution truncated to an unknown halfspace.
method Efficient algorithm using samples and runtime dominated by empirical covariance matrix computation.
result Optimal sample and time complexity bounds for learning a Gaussian under halfspace truncation.
This paper presents a new algorithm, termed \emph{truncated amplitude flow} (TAF), to recover an unknown vector from a system of quadratic equations of the form , where 's are given random measurement vectors. This problem is known to be \emph{NP-hard} in genera…
TKRR improves KRR performance by aligning target functions with kernels.
problem Improving kernel ridge regression performance through target alignment.
method Focuses on truncated kernel ridge regression (TKRR) with an additional spectral truncation parameter.
result TKRR can achieve faster rates than full KRR, reaching parametric rates.
We analyze empirical data from the internet auction site Aukro.cz. The time series of activity shows truncated fractal structure on scales from about 1 minute to about 1 day. The distribution of waiting times as well as the distribution of number of auctions within fixed interval is a power law, with exponents an…
Non-negative matrix factorization (NMF) minimizes the Euclidean distance between the data matrix and its low rank approximation, and it fails when applied to corrupted data because the loss function is sensitive to outliers. In this paper, we propose a Truncated CauchyNMF loss that handle outliers by truncating large e…
As in standard linear regression, in truncated linear regression, we are given access to observations whose dependent variable equals , where is some fixed unknown vector of interest and is independent noise; except we are only given an observation if its dep…
New method evaluates personalized treatment in critical care, robust to death.
problem Truncation by death in critical care makes traditional DTR evaluation ineffective.
method Principal stratification-based approach, focusing on always-survivor value function, with a semiparametrically efficient, multiply robust estimator.
result Demonstrates robustness and efficiency of the method for personalized treatment optimization.
A new algorithm speeds up elliptical slice sampling for truncated multivariate normals.
problem Efficiently sampling from truncated multivariate normal distributions with linear constraints.
method Adapting elliptical slice sampling to linearly truncated multivariate normals, with an algorithm for ellipse-polytope intersection in O(m log m) time.
result The algorithm enhances numerical stability, speeds up running time, and is easy to parallelize.