Transformer-based Parameter Estimation in Statistics

• URL: http://arxiv.org/abs/2403.00019v1
• Date: Wed, 28 Feb 2024 04:30:41 GMT
• Title: Transformer-based Parameter Estimation in Statistics
• Authors: Xiaoxin Yin and David S. Yin
• Abstract summary: We propose a transformer-based approach to parameter estimation. It does not even require knowing the probability density function, which is needed by numerical methods. It is shown that our approach achieves similar or better accuracy as measured by mean-square-errors.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally parameter estimation is done either by closed-form solutions (e.g., maximum likelihood estimation for Gaussian distribution), or by iterative numerical methods such as Newton-Raphson method when closed-form solution does not exist (e.g., for Beta distribution). In this paper we propose a transformer-based approach to parameter estimation. Compared with existing solutions, our approach does not require a closed-form solution or any mathematical derivations. It does not even require knowing the probability density function, which is needed by numerical methods. After the transformer model is trained, only a single inference is needed to estimate the parameters of the underlying distribution based on a sample of observations. In the empirical study we compared our approach with maximum likelihood estimation on commonly used distributions such as normal distribution, exponential distribution and beta distribution. It is shown that our approach achieves similar or better accuracy as measured by mean-square-errors.

Related papers

• Robust Estimation for Kernel Exponential Families with Smoothed Total Variation Distances [2.317910166616341]
  In statistical inference, we commonly assume that samples are independent and identically distributed from a probability distribution. In this paper, we explore the application of GAN-like estimators to a general class of statistical models.
  arXiv  Detail & Related papers  (2024-10-28T05:50:47Z)
• Multivariate root-n-consistent smoothing parameter free matching estimators and estimators of inverse density weighted expectations [51.000851088730684]
  We develop novel modifications of nearest-neighbor and matching estimators which converge at the parametric $sqrt n $-rate. We stress that our estimators do not involve nonparametric function estimators and in particular do not rely on sample-size dependent parameters smoothing.
  arXiv  Detail & Related papers  (2024-07-11T13:28:34Z)
• DistPred: A Distribution-Free Probabilistic Inference Method for Regression and Forecasting [14.390842560217743]
  We propose a novel approach called DistPred for regression and forecasting tasks. We transform proper scoring rules that measure the discrepancy between the predicted distribution and the target distribution into a differentiable discrete form. This allows the model to sample numerous samples in a single forward pass to estimate the potential distribution of the response variable.
  arXiv  Detail & Related papers  (2024-06-17T10:33:00Z)
• Collaborative Heterogeneous Causal Inference Beyond Meta-analysis [68.4474531911361]
  We propose a collaborative inverse propensity score estimator for causal inference with heterogeneous data. Our method shows significant improvements over the methods based on meta-analysis when heterogeneity increases.
  arXiv  Detail & Related papers  (2024-04-24T09:04:36Z)
• Sourcerer: Sample-based Maximum Entropy Source Distribution Estimation [5.673617376471343]
  We propose an approach which targets the maximum entropy distribution, i.e., prioritizes retaining as much uncertainty as possible. Our method is purely sample-based - leveraging the Sliced-Wasserstein distance to measure the discrepancy between the dataset and simulations. To demonstrate the utility of our approach, we infer source distributions for parameters of the Hodgkin-Huxley model from experimental datasets with thousands of single-neuron measurements.
  arXiv  Detail & Related papers  (2024-02-12T17:13:02Z)
• Positive definite nonparametric regression using an evolutionary algorithm with application to covariance function estimation [0.0]
  We propose a novel nonparametric regression framework for estimating covariance functions of stationary processes. Our method can impose positive definiteness, as well as isotropy and monotonicity, on the estimators. Our method provides more reliable estimates for long-range dependence.
  arXiv  Detail & Related papers  (2023-04-25T22:01:14Z)
• Statistical Efficiency of Score Matching: The View from Isoperimetry [96.65637602827942]
  We show a tight connection between statistical efficiency of score matching and the isoperimetric properties of the distribution being estimated. We formalize these results both in the sample regime and in the finite regime.
  arXiv  Detail & Related papers  (2022-10-03T06:09:01Z)
• Nonparametric Conditional Local Independence Testing [69.31200003384122]
  Conditional local independence is an independence relation among continuous time processes. No nonparametric test of conditional local independence has been available. We propose such a nonparametric test based on double machine learning.
  arXiv  Detail & Related papers  (2022-03-25T10:31:02Z)
• Sampling from Arbitrary Functions via PSD Models [55.41644538483948]
  We take a two-step approach by first modeling the probability distribution and then sampling from that model. We show that these models can approximate a large class of densities concisely using few evaluations, and present a simple algorithm to effectively sample from these models.
  arXiv  Detail & Related papers  (2021-10-20T12:25:22Z)
• Characterizations of non-normalized discrete probability distributions and their application in statistics [0.0]
  We derive explicit formulae for the mass functions of discrete probability laws that identify those distributions. Our characterizations, and hence the applications built on them, do not require any knowledge about normalization constants of the probability laws.
  arXiv  Detail & Related papers  (2020-11-09T12:08:12Z)
• Batch Stationary Distribution Estimation [98.18201132095066]
  We consider the problem of approximating the stationary distribution of an ergodic Markov chain given a set of sampled transitions. We propose a consistent estimator that is based on recovering a correction ratio function over the given data.
  arXiv  Detail & Related papers  (2020-03-02T09:10:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.