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Noise-contrastive estimation (NCE) is a statistically consistent method for learning unnormalized probabilistic models. It has been empirically observed that the choice of the noise distribution is crucial for NCE's performance. However,…

Machine Learning · Computer Science 2021-10-22 Bingbin Liu , Elan Rosenfeld , Pradeep Ravikumar , Andrej Risteski

Many parametric statistical models are not properly normalised and only specified up to an intractable partition function, which renders parameter estimation difficult. Examples of unnormalised models are Gibbs distributions, Markov random…

Machine Learning · Statistics 2018-06-12 Ciwan Ceylan , Michael U. Gutmann

Noise Contrastive Estimation (NCE) is a powerful parameter estimation method for log-linear models, which avoids calculation of the partition function or its derivatives at each training step, a computationally demanding step in many cases.…

Computation and Language · Computer Science 2018-09-07 Zhuang Ma , Michael Collins

Noise Contrastive Estimation (NCE) is a popular approach for learning probability density functions parameterized up to a constant of proportionality. The main idea is to design a classification problem for distinguishing training data from…

Machine Learning · Computer Science 2023-03-03 Holden Lee , Chirag Pabbaraju , Anish Sevekari , Andrej Risteski

Self-supervised learning is an increasingly popular approach to unsupervised learning, achieving state-of-the-art results. A prevalent approach consists in contrasting data points and noise points within a classification task: this requires…

Machine Learning · Statistics 2023-01-25 Omar Chehab , Alexandre Gramfort , Aapo Hyvarinen

This paper studies a family of estimators based on noise-contrastive estimation (NCE) for learning unnormalized distributions. The main contribution of this work is to provide a unified perspective on various methods for learning…

Machine Learning · Statistics 2025-07-15 J. Jon Ryu , Abhin Shah , Gregory W. Wornell

Training energy-based models (EBMs) with noise-contrastive estimation (NCE) is theoretically feasible but practically challenging. Effective learning requires the noise distribution to be approximately similar to the target distribution,…

Machine Learning · Computer Science 2022-11-07 Nathaniel Xu

Noise contrastive estimation (NCE) is a popular method for training energy-based models (EBM) with intractable normalisation terms. The key idea of NCE is to learn by comparing unnormalised log-likelihoods of the reference and noisy…

Sound · Computer Science 2025-05-21 Wanli Sun , Anton Ragni

There are many models, often called unnormalized models, whose normalizing constants are not calculated in closed form. Maximum likelihood estimation is not directly applicable to unnormalized models. Score matching, contrastive divergence…

Machine Learning · Statistics 2018-08-27 Masatoshi Uehara , Takeru Matsuda , Fumiyasu Komaki

Noise Contrastive Estimation (NCE) has fueled major breakthroughs in representation learning and generative modeling. Yet a long-standing challenge remains: accurately estimating ratios between distributions that differ substantially, which…

Noise-contrastive estimation (NCE) is a popular method for estimating unnormalised probabilistic models, such as energy-based models, which are effective for modelling complex data distributions. Unlike classical maximum likelihood (ML)…

Machine Learning · Statistics 2024-02-27 Amanda Olmin , Jakob Lindqvist , Lennart Svensson , Fredrik Lindsten

Unnormalised latent variable models are a broad and flexible class of statistical models. However, learning their parameters from data is intractable, and few estimation techniques are currently available for such models. To increase the…

Machine Learning · Statistics 2019-02-26 Benjamin Rhodes , Michael Gutmann

Unsupervised anomaly detection is a challenging task. Autoencoders (AEs) or generative models are often employed to model the data distribution of normal inputs and subsequently identify anomalous, out-of-distribution inputs by high…

Machine Learning · Computer Science 2025-06-12 Yalin Liao , Austin J. Brockmeier

We develop a general method for estimating a finite mixture of non-normalized models. Here, a non-normalized model is defined to be a parametric distribution with an intractable normalization constant. Existing methods for estimating…

Machine Learning · Statistics 2021-09-01 Takeru Matsuda , Aapo Hyvarinen

Learning a parametric model of a data distribution is a well-known statistical problem that has seen renewed interest as it is brought to scale in deep learning. Framing the problem as a self-supervised task, where data samples are…

Machine Learning · Statistics 2022-07-27 Omar Chehab , Alexandre Gramfort , Aapo Hyvarinen

Latent neural stochastic differential equations (SDEs) have recently emerged as a promising approach for learning generative models from stochastic time series data. However, they systematically underestimate the noise level inherent in…

Machine Learning · Computer Science 2025-06-11 Linus Heck , Maximilian Gelbrecht , Michael T. Schaub , Niklas Boers

Recent research has developed several Monte Carlo methods for estimating the normalization constant (partition function) based on the idea of annealing. This means sampling successively from a path of distributions that interpolate between…

Machine Learning · Statistics 2023-10-10 Omar Chehab , Aapo Hyvarinen , Andrej Risteski

Convolutional sparse coding (CSC) can learn representative shift-invariant patterns from multiple kinds of data. However, existing CSC methods can only model noises from Gaussian distribution, which is restrictive and unrealistic. In this…

Machine Learning · Computer Science 2020-04-22 Yaqing Wang , James T. Kwok , Lionel M. Ni

Two recently introduced criteria for estimation of generative models are both based on a reduction to binary classification. Noise-contrastive estimation (NCE) is an estimation procedure in which a generative model is trained to be able to…

Machine Learning · Statistics 2015-05-22 Ian J. Goodfellow

Contrastive representation learning has proven to be an effective self-supervised learning method. Most successful approaches are based on Noise Contrastive Estimation (NCE) and use different views of an instance as positives that should be…

Computer Vision and Pattern Recognition · Computer Science 2023-09-04 Julien Denize , Jaonary Rabarisoa , Astrid Orcesi , Romain Hérault , Stéphane Canu
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