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Register a new userA new method for parameter estimation in probabilistic models: Minimum probability flow
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Fitting probabilistic models to data is often difficult, due to the general intractability of the partition function. We propose a new parameter fitting method, Minimum Probability Flow (MPF), which is applicable to any parametric model. We demonstrate parameter estimation using MPF in two cases: a continuous state space model, and an Ising spin glass. In the latter case it outperforms current techniques by at least an order of magnitude in convergence time with lower error in the recovered coupling parameters.
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Many important classification problems, such as object classification, speech recognition, and machine translation, have been tackled by the supervised learning paradigm in the past, where training corpora of parallel input-output pairs are required with high cost. To remove the need for the parallel training corpora has practical significance for real-world applications, and it is one of the main goals of unsupervised learning. Recently, encouraging progress in unsupervised learning for solving such classification problems has been made and the nature of the challenges has been clarified. In this article, we review this progress and disseminate a class of promising new methods to facilitate understanding the methods for machine learning researchers. In particular, we emphasize the key information that enables the success of unsupervised learning - the sequential statistics as the distributional prior in the labels. Exploitation of such sequential statistics makes it possible to estimate parameters of classifiers without the need of paired input-output data. In this paper, we first introduce the concept of Caesar Cipher and its decryption, which motivated the construction of the novel loss function for unsupervised learning we use throughout the paper. Then we use a simple but representative binary classification task as an example to derive and describe the unsupervised learning algorithm in a step-by-step, easy-to-understand fashion. We include two cases, one with Bigram language model as the sequential statistics for use in unsupervised parameter estimation, and another with a simpler Unigram language model. For both cases, detailed derivation steps for the learning algorithm are included. Further, a summary table compares computational steps of the two cases in executing the unsupervised learning algorithm for learning binary classifiers.
Standard variational lower bounds used to train latent variable models produce biased estimates of most quantities of interest. We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models based on randomized truncation of infinite series. If parameterized by an encoder-decoder architecture, the parameters of the encoder can be optimized to minimize its variance of this estimator. We show that models trained using our estimator give better test-set likelihoods than a standard importance-sampling based approach for the same average computational cost. This estimator also allows use of latent variable models for tasks where unbiased estimators, rather than marginal likelihood lower bounds, are preferred, such as minimizing reverse KL divergences and estimating score functions.
We propose to use deep learning to estimate parameters in statistical models when standard likelihood estimation methods are computationally infeasible. We show how to estimate parameters from max-stable processes, where inference is exceptionally challenging even with small datasets but simulation is straightforward. We use data from model simulations as input and train deep neural networks to learn statistical parameters. Our neural-network-based method provides a competitive alternative to current approaches, as demonstrated by considerable accuracy and computational time improvements. It serves as a proof of concept for deep learning in statistical parameter estimation and can be extended to other estimation problems.
Invertible flow-based generative models are an effective method for learning to generate samples, while allowing for tractable likelihood computation and inference. However, the invertibility requirement restricts models to have the same latent dimensionality as the inputs. This imposes significant architectural, memory, and computational costs, making them more challenging to scale than other classes of generative models such as Variational Autoencoders (VAEs). We propose a generative model based on probability flows that does away with the bijectivity requirement on the model and only assumes injectivity. This also provides another perspective on regularized autoencoders (RAEs), with our final objectives resembling RAEs with specific regularizers that are derived by lower bounding the probability flow objective. We empirically demonstrate the promise of the proposed model, improving over VAEs and AEs in terms of sample quality.
It is often observed that the probabilistic predictions given by a machine learning model can disagree with averaged actual outcomes on specific subsets of data, which is also known as the issue of miscalibration. It is responsible for the unreliability of practical machine learning systems. For example, in online advertising, an ad can receive a click-through rate prediction of 0.1 over some population of users where its actual click rate is 0.15. In such cases, the probabilistic predictions have to be fixed before the system can be deployed. In this paper, we first introduce a new evaluation metric named field-level calibration error that measures the bias in predictions over the sensitive input field that the decision-maker concerns. We show that existing post-hoc calibration methods have limited improvements in the new field-level metric and other non-calibration metrics such as the AUC score. To this end, we propose Neural Calibration, a simple yet powerful post-hoc calibration method that learns to calibrate by making full use of the field-aware information over the validation set. We present extensive experiments on five large-scale datasets. The results showed that Neural Calibration significantly improves against uncalibrated predictions in common metrics such as the negative log-likelihood, Brier score and AUC, as well as the proposed field-level calibration error.
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