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…
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48 results for “truncated data”
New DP framework using data truncation for efficient estimation.
problem Differential privacy in unbounded data support.
method Data truncation, exponential family distributions, maximum likelihood estimation, DP stochastic gradient descent.
result Near-optimal sample complexity for Gaussian mean and covariance estimation.
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.
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.
Bayesian Inference for Left-Truncated Log-Logistic Distributions for Time-to-event Data Analysisstat.ME
Bayesian method estimates LTLL distribution parameters for time-to-event data.
problem Parameter estimation for time-to-event data with left truncation.
method Bayesian inference using Metropolis-Hastings algorithm.
result Bayesian estimation provides more stable and reliable parameter estimates.
Proposes a method to handle sparse multiway count data with false zeros using zero-truncated Poisson regression.
problem Handling sparse multiway count data corrupted by false zeros.
method Zero-truncated Poisson regression with tensor completion.
result Accurate estimation of multiway count data from approximately non-zero counts.
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…
Addressing the Impact of Data Truncation and Parameter Uncertainty on Operational Risk Estimatesq-fin.RM
Typically, operational risk losses are reported above some threshold. This paper studies the impact of ignoring data truncation on the 0.999 quantile of the annual loss distribution for operational risk for a broad range of distribution parameters and truncation levels. Loss frequency and severity are modelled by the P…
The paper investigates the convergence of Vendi scores under finite samples and introduces a truncated version for better performance.
problem The Vendi score's convergence is hindered by computational limitations when using large sample sizes.
method The authors introduce the t-truncated Vendi score to address this issue by truncating the eigenspectrum of the kernel matrix.
result The t-truncated Vendi score converges to its asymptotic limit with a smaller number of samples, improving upon the standard Vendi score.
Paper proposes robust estimators for heavy-tailed data with infinite variance.
problem Developing robust estimators for heavy-tailed data with infinite variance.
method Proposes two robust estimators: ridge log-truncated M-estimator and elastic net log-truncated M-estimator.
result Demonstrates robustness of log-truncated estimations over standard estimations through simulations and real data analysis.
Paper estimates spectral risk measures for insurance data with truncated and censored data.
problem Estimating spectral risk measures for insurance data with left truncation and right censoring.
method Proposes a non-parametric estimator using product limit estimator and establishes asymptotic normality.
result Proposed estimator outperforms existing methods for small k and small sample sizes.
Unified framework for mean testing under truncation bias.
problem High-dimensional mean testing under arbitrary truncation.
method Characterizes fundamental limits and develops a simple second-order test.
result Unified framework connects finite-moment, sub-Gaussian, and median-regular structural regimes.
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 …
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.
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…
We study inference and learning based on a sparse coding model with `spike-and-slab' prior. As in standard sparse coding, the model used assumes independent latent sources that linearly combine to generate data points. However, instead of using a standard sparse prior such as a Laplace distribution, we study the applic…
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.
Nonparametric Bayesian label prediction on a large graph using truncated Laplacian regularizationstat.CO
This article describes an implementation of a nonparametric Bayesian approach to solving binary classification problems on graphs. We consider a hierarchical Bayesian approach with a prior that is constructed by truncating a series expansion of the soft label function using the graph Laplacian eigenfunctions as basis f…
UDN adapts depth to data complexity, outperforming standard neural networks.
problem Adapting neural network depth to data complexity.
method Variational inference for infinitely deep neural networks with a novel algorithm.
result UDN outperforms standard neural networks and other infinite-depth approaches.
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…
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…
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…
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.
PMT uses public data moments to make DP feasible for unbounded data.
problem Applying differential privacy to unbounded data distributions.
method Public-moment-guided Truncation (PMT) using second-moments from public data.
result PMT improves the accuracy and stability of DP models.
Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional sparse data, however, the method suffers from slow convergence and high variance…
Combining data assimilation and machine learning to infer unresolved scale parametrisationphysics.comp-ph
Combines ML and DA to infer unresolved scale parametrisation from noisy data.
problem Training ML-based parametrisations from realistic, noisy and sparse observations.
method Two-step process: DA for state estimation, ML for model error prediction.
result Hybrid model produces better forecasts and attractor representation.
Truncated SGD with heavy-tailed noise eliminates sharp local minima.
problem Avoiding sharp local minima in deep learning models.
method Truncated SGD with heavy-tailed gradient noise.
result Truncated SGD can eliminate sharp local minima entirely from its training trajectory.
Scale-invariant Truncated Lévy Processcond-mat.stat-mech
We develop a scale-invariant truncated Lévy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits Lévy stability for the probability density, and hence shows scaling properties (as observed in empirical data); it has the advantage that all moments are fini…
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.
Paper defines new risk measures for elliptical distributions.
problem Risk measurement for elliptical distributions.
method DTM, DTS, DTK definitions and formula derivation for specific distributions.
result Explicit formulas for DTE, DTV, DTS, and DTK for various distributions.
Derives equations for deep learning biases and weights, showing data complexity reduction.
problem Understanding interpretability in supervised learning.
method Gradient flow equations and dynamical truncation of training data.
result Data complexity reduction at an exponential rate with training.
Kernel ridge regression (KRR) is a well-known and popular nonparametric regression approach with many desirable properties, including minimax rate-optimality in estimating functions that belong to common reproducing kernel Hilbert spaces (RKHS). The approach, however, is computationally intensive for large data sets, d…
Financial Modeling and Option Theory with the Truncated Levy Processcond-mat.stat-mech
In recent studies the truncated Levy process (TLP) has been shown to be very promising for the modeling of financial dynamics. In contrast to the Levy process, the TLP has finite moments and can account for both the previously observed excess kurtosis at short timescales, along with the slow convergence to Gaussian at …
New kernels capture both local and non-local interactions efficiently.
problem Designing kernels that capture both local and non-local interactions while remaining computationally tractable.
method Spectral truncation kernels based on -algebra.
result Spectral truncation kernels induce interactions across the data function domain and reduce computational cost.
Controlling Statistical, Discretization, and Truncation Errors in Learning Fourier Linear Operatorsstat.ML
Study identifies and analyzes three types of errors in learning Fourier operators.
problem Statistical, discretization, and truncation errors in learning Fourier operators.
method Analysis of a Discrete Fourier Transform (DFT) based least squares estimator.
result Established upper and lower bounds on statistical, discretization, and truncation errors.
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.
Faster diffusion-based models generate data with fewer steps.
problem Slow and costly diffusion-based generative models.
method Truncate diffusion process to generate data more efficiently.
result Truncated models provide consistent improvements in performance.
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.
We consider an appoximation of a catenoid constructed from "odd" truncated cones that maintains minimality in a certain sense. Thorough this procedure, we obtain a discrete curve approximating a catenary by exploiting the fact that it is the function that generates a catenoid. In this investigation, the theory of the G…
Constructs classifiers for neural networks with specific data configurations.
problem Finding global minima of deep ReLU neural networks on sequentially separable data.
method Explicitly constructs zero loss neural network classifiers using cumulative parameters and truncation maps.
result Global minimizers can be described with a limited number of parameters based on the data structure.
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.
Tree++ graph kernel captures similarities at multiple granularities.
problem Lack of scale-adaptivity in existing graph kernels.
method Tree++ uses truncated BFS trees and super paths to represent graphs at different granularities.
result Tree++ achieves best classification accuracy on real-world graphs.
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.
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.
The generalized correlation approach, which has been successfully used in statistical radio physics to describe non-Gaussian random processes, is proposed to describe stochastic financial processes. The generalized correlation approach has been used to describe a non-Gaussian random walk with independent, identically d…
New method estimates treatment effects over time for survival data, improving accuracy and smoothness.
problem Estimating treatment effects over time for survival data with left truncation and right censoring.
method surv-iTMLE, a targeted learning procedure for estimating conditional survival probabilities.
result surv-iTMLE outperforms existing methods in bias and smoothness of time-varying effect estimates.
Paper proposes a new model for imputing missing spatiotemporal traffic data.
problem Missing data and sparsity in spatiotemporal traffic data.
method Low-rank tensor completion (LRTC) framework with truncated nuclear norm (TNN).
result The proposed model outperforms state-of-the-art imputation models in various scenarios.
Lower bound shows super-polynomial gap for estimating truncated Gaussian means.
problem Estimating mean of truncated Gaussian distribution with limited samples.
method Statistical Query (SQ) lower bounds for learning.
result Super-polynomial information-computation gap for the task.