24,824 research outputs found
Targeted Undersmoothing
This paper proposes a post-model selection inference procedure, called
targeted undersmoothing, designed to construct uniformly valid confidence sets
for a broad class of functionals of sparse high-dimensional statistical models.
These include dense functionals, which may potentially depend on all elements
of an unknown high-dimensional parameter. The proposed confidence sets are
based on an initially selected model and two additionally selected models, an
upper model and a lower model, which enlarge the initially selected model. We
illustrate application of the procedure in two empirical examples. The first
example considers estimation of heterogeneous treatment effects using data from
the Job Training Partnership Act of 1982, and the second example looks at
estimating profitability from a mailing strategy based on estimated
heterogeneous treatment effects in a direct mail marketing campaign. We also
provide evidence on the finite sample performance of the proposed targeted
undersmoothing procedure through a series of simulation experiments
Feature detection using spikes: the greedy approach
A goal of low-level neural processes is to build an efficient code extracting
the relevant information from the sensory input. It is believed that this is
implemented in cortical areas by elementary inferential computations
dynamically extracting the most likely parameters corresponding to the sensory
signal. We explore here a neuro-mimetic feed-forward model of the primary
visual area (VI) solving this problem in the case where the signal may be
described by a robust linear generative model. This model uses an over-complete
dictionary of primitives which provides a distributed probabilistic
representation of input features. Relying on an efficiency criterion, we derive
an algorithm as an approximate solution which uses incremental greedy inference
processes. This algorithm is similar to 'Matching Pursuit' and mimics the
parallel architecture of neural computations. We propose here a simple
implementation using a network of spiking integrate-and-fire neurons which
communicate using lateral interactions. Numerical simulations show that this
Sparse Spike Coding strategy provides an efficient model for representing
visual data from a set of natural images. Even though it is simplistic, this
transformation of spatial data into a spatio-temporal pattern of binary events
provides an accurate description of some complex neural patterns observed in
the spiking activity of biological neural networks.Comment: This work links Matching Pursuit with bayesian inference by providing
the underlying hypotheses (linear model, uniform prior, gaussian noise
model). A parallel with the parallel and event-based nature of neural
computations is explored and we show application to modelling Primary Visual
Cortex / image processsing.
http://incm.cnrs-mrs.fr/perrinet/dynn/LaurentPerrinet/Publications/Perrinet04tau
- …