990 research outputs found
A power comparison between nonparametric regression tests
In this paper, we consider three major types of nonparametric regression tests that are based on kernel and local polynomial smoothing techniques. Their asymptotic power comparisons are established systematically under the fixed and contiguous alternatives, and are also illustrated through non-asymptotic investigations and finite-sample simulation studies. --Goodness-of-fit,Local alternative,Local polynomial regression,Power,Smoothing parameter
Multiple testing via for large-scale imaging data
The multiple testing procedure plays an important role in detecting the
presence of spatial signals for large-scale imaging data. Typically, the
spatial signals are sparse but clustered. This paper provides empirical
evidence that for a range of commonly used control levels, the conventional
procedure can lack the ability to detect statistical
significance, even if the -values under the true null hypotheses are
independent and uniformly distributed; more generally, ignoring the neighboring
information of spatially structured data will tend to diminish the detection
effectiveness of the procedure. This paper first
introduces a scalar quantity to characterize the extent to which the "lack of
identification phenomenon" () of the
procedure occurs. Second, we propose a new multiple comparison procedure,
called , to accommodate the spatial information of
neighboring -values, via a local aggregation of -values. Theoretical
properties of the procedure are investigated under weak
dependence of -values. It is shown that the
procedure alleviates the of the
procedure, thus substantially facilitating the selection of more stringent
control levels. Simulation evaluations indicate that the procedure improves the detection sensitivity of the procedure with little loss in detection specificity. The computational
simplicity and detection effectiveness of the procedure
are illustrated through a real brain fMRI dataset.Comment: Published in at http://dx.doi.org/10.1214/10-AOS848 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Bump hunting with non-Gaussian kernels
It is well known that the number of modes of a kernel density estimator is
monotone nonincreasing in the bandwidth if the kernel is a Gaussian density.
There is numerical evidence of nonmonotonicity in the case of some non-Gaussian
kernels, but little additional information is available. The present paper
provides theoretical and numerical descriptions of the extent to which the
number of modes is a nonmonotone function of bandwidth in the case of general
compactly supported densities. Our results address popular kernels used in
practice, for example, the Epanechnikov, biweight and triweight kernels, and
show that in such cases nonmonotonicity is present with strictly positive
probability for all sample sizes n\geq3. In the Epanechnikov and biweight cases
the probability of nonmonotonicity equals 1 for all n\geq2. Nevertheless, in
spite of the prevalence of lack of monotonicity revealed by these results, it
is shown that the notion of a critical bandwidth (the smallest bandwidth above
which the number of modes is guaranteed to be monotone) is still well defined.
Moreover, just as in the Gaussian case, the critical bandwidth is of the same
size as the bandwidth that minimises mean squared error of the density
estimator. These theoretical results, and new numerical evidence, show that the
main effects of nonmonotonicity occur for relatively small bandwidths, and have
negligible impact on many aspects of bump hunting.Comment: Published at http://dx.doi.org/10.1214/009053604000000715 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A Power Comparison Between Nonparametric Regression Tests
In this paper, we consider three major types of nonparametric regression tests that are based on kernel and local polynomial smoothing techniques. Their asymptotic power comparisons are established systematically under the fixed and contiguous alternatives, and are also illustrated through non-asymptotic investigations and finite-sample simulation studies
Spiking sampling network for image sparse representation and dynamic vision sensor data compression
Sparse representation has attracted great attention because it can greatly
save storage resources and find representative features of data in a
low-dimensional space. As a result, it may be widely applied in engineering
domains including feature extraction, compressed sensing, signal denoising,
picture clustering, and dictionary learning, just to name a few. In this paper,
we propose a spiking sampling network. This network is composed of spiking
neurons, and it can dynamically decide which pixel points should be retained
and which ones need to be masked according to the input. Our experiments
demonstrate that this approach enables better sparse representation of the
original image and facilitates image reconstruction compared to random
sampling. We thus use this approach for compressing massive data from the
dynamic vision sensor, which greatly reduces the storage requirements for event
data
Adversarial Defense via Neural Oscillation inspired Gradient Masking
Spiking neural networks (SNNs) attract great attention due to their low power
consumption, low latency, and biological plausibility. As they are widely
deployed in neuromorphic devices for low-power brain-inspired computing,
security issues become increasingly important. However, compared to deep neural
networks (DNNs), SNNs currently lack specifically designed defense methods
against adversarial attacks. Inspired by neural membrane potential oscillation,
we propose a novel neural model that incorporates the bio-inspired oscillation
mechanism to enhance the security of SNNs. Our experiments show that SNNs with
neural oscillation neurons have better resistance to adversarial attacks than
ordinary SNNs with LIF neurons on kinds of architectures and datasets.
Furthermore, we propose a defense method that changes model's gradients by
replacing the form of oscillation, which hides the original training gradients
and confuses the attacker into using gradients of 'fake' neurons to generate
invalid adversarial samples. Our experiments suggest that the proposed defense
method can effectively resist both single-step and iterative attacks with
comparable defense effectiveness and much less computational costs than
adversarial training methods on DNNs. To the best of our knowledge, this is the
first work that establishes adversarial defense through masking surrogate
gradients on SNNs
A noise based novel strategy for faster SNN training
Spiking neural networks (SNNs) are receiving increasing attention due to
their low power consumption and strong bio-plausibility. Optimization of SNNs
is a challenging task. Two main methods, artificial neural network (ANN)-to-SNN
conversion and spike-based backpropagation (BP), both have their advantages and
limitations. For ANN-to-SNN conversion, it requires a long inference time to
approximate the accuracy of ANN, thus diminishing the benefits of SNN. With
spike-based BP, training high-precision SNNs typically consumes dozens of times
more computational resources and time than their ANN counterparts. In this
paper, we propose a novel SNN training approach that combines the benefits of
the two methods. We first train a single-step SNN(T=1) by approximating the
neural potential distribution with random noise, then convert the single-step
SNN(T=1) to a multi-step SNN(T=N) losslessly. The introduction of Gaussian
distributed noise leads to a significant gain in accuracy after conversion. The
results show that our method considerably reduces the training and inference
times of SNNs while maintaining their high accuracy. Compared to the previous
two methods, ours can reduce training time by 65%-75% and achieves more than
100 times faster inference speed. We also argue that the neuron model augmented
with noise makes it more bio-plausible
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