No file available
To read the file of this research,
you can request a copy directly from the authors.
Transformers Can Do Bayesian Inference
Preprints and early-stage research may not have been peer reviewed yet.
Abstract
Currently, it is hard to reap the benefits of deep learning for Bayesian methods, which allow the explicit specification of prior knowledge and accurately capture model uncertainty. We present Prior-Data Fitted Networks (PFNs). PFNs leverage large-scale machine learning techniques to approximate a large set of posteriors. The only requirement for PFNs to work is the ability to sample from a prior distribution over supervised learning tasks (or functions). Our method restates the objective of posterior approximation as a supervised classification problem with a set-valued input: it repeatedly draws a task (or function) from the prior, draws a set of data points and their labels from it, masks one of the labels and learns to make probabilistic predictions for it based on the set-valued input of the rest of the data points. Presented with a set of samples from a new supervised learning task as input, PFNs make probabilistic predictions for arbitrary other data points in a single forward propagation, having learned to approximate Bayesian inference. We demonstrate that PFNs can near-perfectly mimic Gaussian processes and also enable efficient Bayesian inference for intractable problems, with over 200-fold speedups in multiple setups compared to current methods. We obtain strong results in very diverse areas such as Gaussian process regression, Bayesian neural networks, classification for small tabular data sets, and few-shot image classification, demonstrating the generality of PFNs. Code and trained PFNs are released at https://github.com/automl/TransformersCanDoBayesianInference.
... PFNs challenge traditional model training by embracing a vast knowledge base derived from simulated datasets, enabling rapid and insightful inference on new data. Key concepts of PFNs include: Prior-Data Fitted Networks (PFNs) 19 challenge the traditional model training paradigm with a Bayesian-inspired approach. Instead of relying on a single training dataset, PFNs leverage knowledge from a vast collection of simulated datasets. ...
... Concept of prior-data fitted networks (PFNs).19 ...
Objective
This study aims to create a robust and interpretable method for predicting dementia in Parkinson's disease (PD), especially in resource-limited settings. The model aims to be accurate even with small datasets and missing values, ultimately promoting its use in clinical practice to benefit patients and medical professionals.
Methods
Our study introduces LightGBM–TabPFN, a novel hybrid model for predicting dementia conversion in PD. Combining LightGBM's strength in handling missing values with TabPFN's ability to exploit small datasets, LightGBM–TabPFN outperforms seven existing methods, achieving outstanding accuracy and interpretability thanks to SHAP analysis. This analysis leverages data from 242 PD patients across 17 variables.
Results
Our LightGBM–TabPFN model significantly outperformed seven existing methods. Achieving an accuracy of 0.9592 and an area under the ROC curve of 0.9737.
Conclusions
The interpretable LightGBM–TabPFN with SHAP signifies a significant advancement in predictive modeling for neurodegenerative diseases. This study not only improves dementia prediction in PD but also provides clinical professionals with insights into model predictions, offering opportunities for application in clinical settings.
... TabPFN is a PFN [32] model developed by Hollman et al. [33]. It is used for performing supervised classification tasks on tabular data. ...
The industrial internet of things (IIoT) has undergone rapid growth in recent years, which has resulted in an increase in the number of threats targeting both IIoT devices and their connecting technologies. However, deploying tools to counter these threats involves tackling inherent limitations, such as limited processing power, memory, and network bandwidth. As a result, traditional solutions, such as the ones used for desktop computers or servers, cannot be applied directly in the IIoT, and the development of new technologies is essential to overcome this issue. One approach that has shown potential for this new paradigm is the implementation of intrusion detection system (IDS) that rely on machine learning (ML) techniques. These IDSs can be deployed in the industrial control system or even at the edge layer of the IIoT topology. However, one of their drawbacks is that, depending on the factory’s specifications, it can be quite challenging to locate sufficient traffic data to train these models. In order to address this problem, this study introduces a novel IDS based on the TabPFN model, which can operate on small datasets of IIoT traffic and protocols, as not in general much traffic is generated in this environment. To assess its efficacy, it is compared against other ML algorithms, such as random forest, XGBoost, and LightGBM, by evaluating each method with different training set sizes and varying numbers of classes to classify. Overall, TabPFN produced the most promising outcomes, with a 10–20% differentiation in each metric. The best performance was observed when working with 1000 training set samples, obtaining an F1 score of 81% for 6-class classification and 72% for 10-class classification.
This purpose of this introductory paper is threefold. First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the main building blocks of modern Markov chain Monte Carlo simulation, thereby providing and introduction to the remaining papers of this special issue. Lastly, it discusses new interesting research horizons.
The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building large-scale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide variety of algorithms — among them sum-product, cluster variational methods, expectation-propagation, mean field methods, max-product and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.
The ability of learning networks to generalize can be greatly enhanced by providing constraints from the task domain. This paper demonstrates how such constraints can be integrated into a backpropagation network through the architecture of the network. This approach has been successfully applied to the recognition of handwritten zip code digits provided by the U.S. Postal Service. A single network learns the entire recognition operation, going from the normalized image of the character to the final classification.
A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks. The framework makes possible (1) objective comparisons between solutions using alternative network architectures, (2) objective stopping rules for network pruning or growing procedures, (3) objective choice of magnitude and type of weight decay terms or additive regularizers (for penalizing large weights, etc.), (4) a measure of the effective number of well-determined parameters in a model, (5) quantified estimates of the error bars on network parameters and on network output, and (6) objective comparisons with alternative learning and interpolation models such as splines and radial basis functions. The Bayesian "evidence" automatically embodies "Occam's razor," penalizing overflexible and overcomplex models. The Bayesian approach helps detect poor underlying assumptions in learning models. For learning models well matched to a problem, a good correlation between generalization ability and the Bayesian evidence is obtained.
In meta-learning an agent extracts knowledge from observed tasks, aiming to facilitate learning of novel future tasks. Under the assumption that future tasks are ‘related’ to previous tasks, accumulated knowledge should be learned in such a way that they capture the common structure across learned tasks, while allowing the learner sufficient flexibility to adapt to novel aspects of a new task. We present a framework for meta-learning that is based on generalization error bounds, allowing us to extend various PAC-Bayes bounds to meta-learning. Learning takes place through the construction of a distribution over hypotheses based on the observed tasks, and its utilization for learning a new task. Thus, prior knowledge is incorporated through setting an experience-dependent prior for novel tasks. We develop a gradient-based algorithm, and implement it for deep neural networks, based on minimizing an objective function derived from the bounds, and demonstrate its effectiveness numerically. In addition to establishing the improved performance available through meta-learning, we demonstrate the intuitive way by which prior information is manifested at different levels of the network.
Restart techniques are common in gradient-free optimization to deal with multimodal functions. Partial restarts are also gaining popularity in gradient-based optimization to improve the rate of convergence in accelerated gradient schemes to deal with ill-conditioned functions. In this paper, we propose a simple restart technique for stochastic gradient descent to improve its anytime performance when training deep neural networks. We empirically study its performance on CIFAR-10 and CIFAR-100 datasets where we demonstrate new state-of-the-art results below 4backslash% and 19backslash%, respectively. Our source code is available at https://github.com/loshchil/SGDR.
We propose a general purpose variational inference algorithm that forms a natural counterpart of gradient descent for optimization. Our method iteratively transports a set of particles to match the target distribution, by applying a form of functional gradient descent that minimizes the KL divergence. Empirical studies are performed on various real world models and datasets, on which our method is competitive with existing state-of-the-art methods. The derivation of our method is based on a new theoretical result that connects the derivative of KL divergence under smooth transforms with Stein's identity and a recently proposed kernelized Stein discrepancy, which is of independent interest.
The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.0 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.
Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior over parameters by conditioning on data being inside an -ball around the observed data, which is only correct in the limit . Monte Carlo methods can then draw samples from the approximate posterior to approximate predictions or error bars on parameters. These algorithms critically slow down as , and in practice draw samples from a broader distribution than the posterior. We propose a new approach to likelihood-free inference based on Bayesian conditional density estimation. Preliminary inferences based on limited simulation data are used to guide later simulations. In some cases, learning an accurate parametric representation of the entire true posterior distribution requires fewer model simulations than Monte Carlo ABC methods need to produce a single sample from an approximate posterior.
One of the core problems of modern statistics is to approximate
difficult-to-compute probability distributions. This problem is especially
important in Bayesian statistics, which frames all inference about unknown
quantities as a calculation about the posterior. In this paper, we review
variational inference (VI), a method from machine learning that approximates
probability distributions through optimization. VI has been used in myriad
applications and tends to be faster than classical methods, such as Markov
chain Monte Carlo sampling. The idea behind VI is to first posit a family of
distributions and then to find the member of that family which is close to the
target. Closeness is measured by Kullback-Leibler divergence. We review the
ideas behind mean-field variational inference, discuss the special case of VI
applied to exponential family models, present a full example with a Bayesian
mixture of Gaussians, and derive a variant that uses stochastic optimization to
scale up to massive data. We discuss modern research in VI and highlight
important open problems. VI is powerful, but it is not yet well understood. Our
hope in writing this paper is to catalyze statistical research on this
widely-used class of algorithms.
People learning new concepts can often generalize successfully from just a single example, yet machine learning algorithms
typically require tens or hundreds of examples to perform with similar accuracy. People can also use learned concepts in richer
ways than conventional algorithms—for action, imagination, and explanation. We present a computational model that captures
these human learning abilities for a large class of simple visual concepts: handwritten characters from the world’s alphabets.
The model represents concepts as simple programs that best explain observed examples under a Bayesian criterion. On a challenging
one-shot classification task, the model achieves human-level performance while outperforming recent deep learning approaches.
We also present several “visual Turing tests” probing the model’s creative generalization abilities, which in many cases are
indistinguishable from human behavior.
Two features distinguish the Bayesian approach to learning models from data. First, beliefs derived from background knowledge are used to select a prior probability distribution for the model parameters. Second, predictions of future observations are made by integrating the model's predictions with respect to the posterior parameter distribution obtained by updating this prior to take account of the data. For neural network models, both these aspects present diiculties | the prior over network parameters has no obvious relation to our prior knowledge, and integration over the posterior is computationally very demanding. I address the problem by deening classes of prior distributions for network param-eters that reach sensible limits as the size of the network goes to innnity. In this limit, the properties of these priors can be elucidated. Some priors converge to Gaussian processes, in which functions computed by the network may be smooth, Brownian, or fractionally Brownian. Other priors converge to non-Gaussian stable processes. Interesting eeects are obtained by combining priors of both sorts in networks with more than one hidden layer.
In this paper we propose a new framework for learning from large scale datasets based on iterative learning from small mini-batches. By adding the right amount of noise to a standard stochastic gradient optimization algorithm we show that the iterates will converge to samples from the true posterior distribution as we anneal the stepsize. This seamless transition between optimization and Bayesian posterior sampling provides an inbuilt protection against overfitting. We also propose a practical method for Monte Carlo estimates of posterior statistics which monitors a “sampling threshold ” and collects samples after it has been surpassed. We apply the method to three models: a mixture of Gaussians, logistic regression and ICA with natural gradients. 1.
BoTorch: A Framework for Efficient Monte-Carlo Bayesian Optimization
- Maximilian Balandat
- Brian Karrer
- Daniel R Jiang
- Samuel Daulton
- Benjamin Letham
- Andrew Gordon Wilson
- Eytan Bakshy
Maximilian Balandat, Brian Karrer, Daniel R. Jiang, Samuel Daulton, Benjamin Letham, Andrew Gordon Wilson, and Eytan Bakshy. BoTorch: A Framework for Efficient Monte-Carlo
Bayesian Optimization. In Advances in Neural Information Processing Systems 33, 2020.
A distributional perspective on reinforcement learning
- Will Marc G Bellemare
- Rémi Dabney
- Munos
Marc G Bellemare, Will Dabney, and Rémi Munos. A distributional perspective on reinforcement
learning. In International Conference on Machine Learning, pp. 449-458. PMLR, 2017.
Pyro: Deep Universal Probabilistic Programming
- Eli Bingham
- Jonathan P Chen
- Martin Jankowiak
- Fritz Obermeyer
- Neeraj Pradhan
- Theofanis Karaletsos
- Rohit Singh
- Paul Szerlip
- Paul Horsfall
- Noah D Goodman
Eli Bingham, Jonathan P. Chen, Martin Jankowiak, Fritz Obermeyer, Neeraj Pradhan, Theofanis
Karaletsos, Rohit Singh, Paul Szerlip, Paul Horsfall, and Noah D. Goodman. Pyro: Deep Universal
Probabilistic Programming. Journal of Machine Learning Research, 2018.
Darts: Differentiable architecture search
- Hanxiao Liu
- Karen Simonyan
- Yiming Yang
Hanxiao Liu, Karen Simonyan, and Yiming Yang. Darts: Differentiable architecture search. In
International Conference on Learning Representations, 2018.
Benchmarking simulation-based inference
- Jan-Matthis Lueckmann
- Jan Boelts
- David Greenberg
- Pedro Goncalves
- Jakob Macke
Jan-Matthis Lueckmann, Jan Boelts, David Greenberg, Pedro Goncalves, and Jakob Macke. Benchmarking simulation-based inference. In International Conference on Artificial Intelligence and
Statistics, pp. 343-351. PMLR, 2021.
Obtaining well calibrated probabilities using bayesian binning
- Gregory F Mahdi Pakdaman Naeini
- Milos Cooper
- Hauskrecht
Mahdi Pakdaman Naeini, Gregory F. Cooper, and Milos Hauskrecht. Obtaining well calibrated
probabilities using bayesian binning. In Proceedings of the Twenty-Ninth AAAI Conference on
Artificial Intelligence, AAAI'15, pp. 2901-2907. AAAI Press, 2015. ISBN 0262511290.
Catboost: Unbiased boosting with categorical features
- Liudmila Prokhorenkova
- Gleb Gusev
- Aleksandr Vorobev
- Anna Veronika Dorogush
- Andrey Gulin
Liudmila Prokhorenkova, Gleb Gusev, Aleksandr Vorobev, Anna Veronika Dorogush, and Andrey
Gulin. Catboost: Unbiased boosting with categorical features. In Proceedings of the 32nd
International Conference on Neural Information Processing Systems, NIPS'18, pp. 6639-6649,
Red Hook, NY, USA, 2018. Curran Associates Inc.
Bayesian model-agnostic meta-learning
- Jaesik Yoon
- Taesup Kim
- Ousmane Dia
- Sungwoong Kim
- Yoshua Bengio
- Sungjin Ahn
Jaesik Yoon, Taesup Kim, Ousmane Dia, Sungwoong Kim, Yoshua Bengio, and Sungjin Ahn.
Bayesian model-agnostic meta-learning. In Proceedings of the 32nd International Conference on
Neural Information Processing Systems, pp. 7343-7353, 2018.
- Sheheryar Zaidi
- Arber Zela
- Thomas Elsken
- Chris Holmes
- Frank Hutter
- Yee Whye Teh
Sheheryar Zaidi, Arber Zela, Thomas Elsken, Chris Holmes, Frank Hutter, and Yee Whye Teh. Neural
ensemble search for uncertainty estimation and dataset shift. arXiv preprint arXiv:2006.08573,
2020.
Bayesnas: A bayesian approach for neural architecture search
- Hongpeng Zhou
- Minghao Yang
- Jun Wang
- Wei Pan
Hongpeng Zhou, Minghao Yang, Jun Wang, and Wei Pan. Bayesnas: A bayesian approach for neural
architecture search. CoRR, abs/1905.04919, 2019.