We provide an efficient algorithm for the classical problem, going back to Galton, Pearson, and Fisher, of estimating, with arbitrary accuracy the parameters of a multivariate normal distribution from truncated samples. Truncated samples from a -variate normal means a samples is only re…
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48 results for “hidden truncation”
The paper improves asset allocation using a skew-normal distribution in the Black-Litterman model.
problem Improving asset allocation under skewed return distributions.
method Using the Black-Litterman model with hidden truncation skew-normal distribution and Simaan's three-moment risk model.
result Optimal portfolios have less risk and higher skewness compared to classical BL model.
We present a probabilistic framework for nonlinearities, based on doubly truncated Gaussian distributions. By setting the truncation points appropriately, we are able to generate various types of nonlinearities within a unified framework, including sigmoid, tanh and ReLU, the most commonly used nonlinearities in neural…
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.
Convergence Analysis of Real-time Recurrent Learning (RTRL) for a class of Recurrent Neural Networkscs.LG
RTRL optimizes long sequences without truncation, converging to loss minima.
problem Inaccuracies in TBPTT for long sequences.
method Online optimization with exact gradient calculation.
result RTRL converges to loss minima for a class of RNNs.
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…
Study evaluates initialization strategies for infinite hidden Markov models.
problem Limited attention to initialization in infinite hidden Markov models.
method Systematically evaluated distance-based clustering, model-based, and uniform initializations.
result Distance-based clustering initializations consistently outperform other methods.
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 this letter we borrow from the inference techniques developed for unbounded state-cardinality (nonparametric) variants of the HMM and use them to develop a tuning-parameter free, black-box inference procedure for Explicit-state-duration hidden Markov models (EDHMM). EDHMMs are HMMs that have latent states consisting…
The paper constructs minimizers for deep learning networks and analyzes their geometric structure.
problem Underparametrized deep learning networks and their minimizers.
method Direct construction of minimizers without gradient descent, considering specific settings.
result Explicit family of minimizers for the global minimum and a set of degenerate local minima.
Gaussian graphical models (GGMs) are widely used for statistical modeling, because of ease of inference and the ubiquitous use of the normal distribution in practical approximations. However, they are also known for their limited modeling abilities, due to the Gaussian assumption. In this paper, we introduce a novel va…
A new method reduces variance in PG methods for RL, improving efficiency and convergence.
problem Improving sample efficiency and convergence of policy gradient methods in reinforcement learning.
method Proposes a gradient truncation mechanism and designs TSIVR-PG method to maximize rewards and utility.
result Shows sample complexity of TSIVR-PG to find ε-stationary policy and global ε-optimal policy.
A new framework predicts hidden Markov model regimes online.
problem Efficiently identify hidden Markov model regimes in streaming data.
method Develops a predictive-first optimisation framework for streaming HMMs, approximating the full posterior predictive distribution.
result The method provides competitive prequential performance compared to Online EM and Sequential Monte Carlo.
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.
Functional connectivity refers to the temporal statistical relationship between spatially distinct brain regions and is usually inferred from the time series coherence/correlation in brain activity between regions of interest. In human functional brain networks, the network structure is often inferred from functional m…
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…
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.
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.
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…
Genetic sequence data are well described by hidden Markov models (HMMs) in which latent states correspond to clusters of similar mutation patterns. Theory from statistical genetics suggests that these HMMs are nonhomogeneous (their transition probabilities vary along the chromosome) and have large support for self tran…
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.
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.
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.
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.
Deep learning methods have recently achieved great empirical success on machine translation, dialogue response generation, summarization, and other text generation tasks. At a high level, the technique has been to train end-to-end neural network models consisting of an encoder model to produce a hidden representation o…
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 …
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…
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.
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…
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.
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.
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…
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.
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…
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.
We show that generalised geometry gives a unified description of maximally supersymmetric consistent truncations of ten- and eleven-dimensional supergravity. In all cases the reduction manifold admits a "generalised parallelisation" with a frame algebra with constant coefficients. The consistent truncation then arises …
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.
Adaptive Nucleus Truncation Improves Long-Form Reasoning
problem Improving long-form reasoning in language models
method Adaptive Nucleus Truncation Sampling (ANTS)
result Significant performance gains across various benchmarks
The paper studies deformation spaces of Coxeter truncation polytopes.
problem Understanding the geometric properties and deformations of Coxeter truncation polytopes.
method Analyzing Coxeter truncation polytopes and their deformation spaces.
result Description of deformation spaces for Coxeter truncation polytopes of dimension .
Estimates inverse temperature of Ising models with a single sample.
problem Estimating inverse temperature in truncated Ising models with hard constraints.
method Maximizing pseudolikelihood to estimate the inverse temperature.
result An estimator that is nearly time and -consistent.
The paper connects quantum -symbols to tetrahedra volumes via discrete Fourier transforms.
problem Understanding the asymptotic behavior of quantum -symbols and their relation to 3-manifold invariants.
method Proposing and proving a conjecture linking discrete Fourier transforms of quantum -symbols to the volumes of deeply truncated tetrahedra.
result Supporting evidence for the conjecture in specific cases, with numerical calculations for larger dihedral angles.
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…