Основні поняття
Bayesian Additive Regression Networks (BARN) is a flexible and robust approach to nonlinear regression that combines the strengths of Bayesian Additive Regression Trees (BART) and modern neural networks.
Анотація
The key highlights and insights from the content are:
BARN adapts the MCMC model sampling process of BART to modern neural networks, leveraging the strengths of both approaches.
BARN replaces the ensemble of decision trees in BART with an ensemble of small neural networks, each with a single hidden layer.
The MCMC procedure in BARN modifies the architecture of the neural networks by adding or subtracting neurons, effectively performing neural architecture search.
BARN approximates the posterior distribution of the neural networks by using the likelihood of the peak weights, rather than computing the full integral, to make the calculations tractable.
Empirical evaluation on benchmark regression problems and synthetic data sets shows that BARN often outperforms shallow neural networks, BART, and ordinary least squares in terms of lower test error and better fit, while being more robust across a variety of problem settings.
BARN's performance comes at the cost of greater computation time compared to some other methods, but it can still be competitive when hyperparameter tuning is not required.
The authors discuss potential future work to improve the theoretical understanding and practical implementation of BARN, such as deriving more rigorous MCMC transition probabilities, better justifying the model size prior, and exploring extensions to classification problems or architecture search.
Статистика
We apply Bayesian Additive Regression Tree (BART) principles to training an ensemble of small neural networks for regression tasks.
Using Markov Chain Monte Carlo, we sample from the posterior distribution of neural networks that have a single hidden layer.
On test data benchmarks, BARN averaged between 5% to 20% lower root mean square error compared to other methods.
Цитати
"BARN provides more consistent and often more accurate results. On test data benchmarks, BARN averaged between 5% to 20% lower root mean square error."
"BARN sometimes takes on the order of a minute where competing methods take a second or less. But, BARN without cross-validated hyperparameter tuning takes about the same amount of computation time as tuned other methods."