26,902 research outputs found
Lightweight Probabilistic Deep Networks
Even though probabilistic treatments of neural networks have a long history,
they have not found widespread use in practice. Sampling approaches are often
too slow already for simple networks. The size of the inputs and the depth of
typical CNN architectures in computer vision only compound this problem.
Uncertainty in neural networks has thus been largely ignored in practice,
despite the fact that it may provide important information about the
reliability of predictions and the inner workings of the network. In this
paper, we introduce two lightweight approaches to making supervised learning
with probabilistic deep networks practical: First, we suggest probabilistic
output layers for classification and regression that require only minimal
changes to existing networks. Second, we employ assumed density filtering and
show that activation uncertainties can be propagated in a practical fashion
through the entire network, again with minor changes. Both probabilistic
networks retain the predictive power of the deterministic counterpart, but
yield uncertainties that correlate well with the empirical error induced by
their predictions. Moreover, the robustness to adversarial examples is
significantly increased.Comment: To appear at CVPR 201
Kernel Bayes' rule
A nonparametric kernel-based method for realizing Bayes' rule is proposed,
based on representations of probabilities in reproducing kernel Hilbert spaces.
Probabilities are uniquely characterized by the mean of the canonical map to
the RKHS. The prior and conditional probabilities are expressed in terms of
RKHS functions of an empirical sample: no explicit parametric model is needed
for these quantities. The posterior is likewise an RKHS mean of a weighted
sample. The estimator for the expectation of a function of the posterior is
derived, and rates of consistency are shown. Some representative applications
of the kernel Bayes' rule are presented, including Baysian computation without
likelihood and filtering with a nonparametric state-space model.Comment: 27 pages, 5 figure
Sequential Bayesian inference for static parameters in dynamic state space models
A method for sequential Bayesian inference of the static parameters of a
dynamic state space model is proposed. The method is based on the observation
that many dynamic state space models have a relatively small number of static
parameters (or hyper-parameters), so that in principle the posterior can be
computed and stored on a discrete grid of practical size which can be tracked
dynamically. Further to this, this approach is able to use any existing
methodology which computes the filtering and prediction distributions of the
state process. Kalman filter and its extensions to non-linear/non-Gaussian
situations have been used in this paper. This is illustrated using several
applications: linear Gaussian model, Binomial model, stochastic volatility
model and the extremely non-linear univariate non-stationary growth model.
Performance has been compared to both existing on-line method and off-line
methods
Bayesian Conditional Density Filtering
We propose a Conditional Density Filtering (C-DF) algorithm for efficient
online Bayesian inference. C-DF adapts MCMC sampling to the online setting,
sampling from approximations to conditional posterior distributions obtained by
propagating surrogate conditional sufficient statistics (a function of data and
parameter estimates) as new data arrive. These quantities eliminate the need to
store or process the entire dataset simultaneously and offer a number of
desirable features. Often, these include a reduction in memory requirements and
runtime and improved mixing, along with state-of-the-art parameter inference
and prediction. These improvements are demonstrated through several
illustrative examples including an application to high dimensional compressed
regression. Finally, we show that C-DF samples converge to the target posterior
distribution asymptotically as sampling proceeds and more data arrives.Comment: 41 pages, 7 figures, 12 table
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