73 research outputs found
Particle Gibbs for Bayesian Additive Regression Trees
Additive regression trees are flexible non-parametric models and popular
off-the-shelf tools for real-world non-linear regression. In application
domains, such as bioinformatics, where there is also demand for probabilistic
predictions with measures of uncertainty, the Bayesian additive regression
trees (BART) model, introduced by Chipman et al. (2010), is increasingly
popular. As data sets have grown in size, however, the standard
Metropolis-Hastings algorithms used to perform inference in BART are proving
inadequate. In particular, these Markov chains make local changes to the trees
and suffer from slow mixing when the data are high-dimensional or the best
fitting trees are more than a few layers deep. We present a novel sampler for
BART based on the Particle Gibbs (PG) algorithm (Andrieu et al., 2010) and a
top-down particle filtering algorithm for Bayesian decision trees
(Lakshminarayanan et al., 2013). Rather than making local changes to individual
trees, the PG sampler proposes a complete tree to fit the residual. Experiments
show that the PG sampler outperforms existing samplers in many settings
Mondrian Forests for Large-Scale Regression when Uncertainty Matters
Many real-world regression problems demand a measure of the uncertainty
associated with each prediction. Standard decision forests deliver efficient
state-of-the-art predictive performance, but high-quality uncertainty estimates
are lacking. Gaussian processes (GPs) deliver uncertainty estimates, but
scaling GPs to large-scale data sets comes at the cost of approximating the
uncertainty estimates. We extend Mondrian forests, first proposed by
Lakshminarayanan et al. (2014) for classification problems, to the large-scale
non-parametric regression setting. Using a novel hierarchical Gaussian prior
that dovetails with the Mondrian forest framework, we obtain principled
uncertainty estimates, while still retaining the computational advantages of
decision forests. Through a combination of illustrative examples, real-world
large-scale datasets, and Bayesian optimization benchmarks, we demonstrate that
Mondrian forests outperform approximate GPs on large-scale regression tasks and
deliver better-calibrated uncertainty assessments than decision-forest-based
methods.Comment: Proceedings of the 19th International Conference on Artificial
Intelligence and Statistics (AISTATS) 2016, Cadiz, Spain. JMLR: W&CP volume
5
Do Deep Generative Models Know What They Don't Know?
A neural network deployed in the wild may be asked to make predictions for
inputs that were drawn from a different distribution than that of the training
data. A plethora of work has demonstrated that it is easy to find or synthesize
inputs for which a neural network is highly confident yet wrong. Generative
models are widely viewed to be robust to such mistaken confidence as modeling
the density of the input features can be used to detect novel,
out-of-distribution inputs. In this paper we challenge this assumption. We find
that the density learned by flow-based models, VAEs, and PixelCNNs cannot
distinguish images of common objects such as dogs, trucks, and horses (i.e.
CIFAR-10) from those of house numbers (i.e. SVHN), assigning a higher
likelihood to the latter when the model is trained on the former. Moreover, we
find evidence of this phenomenon when pairing several popular image data sets:
FashionMNIST vs MNIST, CelebA vs SVHN, ImageNet vs CIFAR-10 / CIFAR-100 / SVHN.
To investigate this curious behavior, we focus analysis on flow-based
generative models in particular since they are trained and evaluated via the
exact marginal likelihood. We find such behavior persists even when we restrict
the flows to constant-volume transformations. These transformations admit some
theoretical analysis, and we show that the difference in likelihoods can be
explained by the location and variances of the data and the model curvature.
Our results caution against using the density estimates from deep generative
models to identify inputs similar to the training distribution until their
behavior for out-of-distribution inputs is better understood.Comment: ICLR 201
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