29,765 research outputs found
On The Robustness of a Neural Network
With the development of neural networks based machine learning and their
usage in mission critical applications, voices are rising against the
\textit{black box} aspect of neural networks as it becomes crucial to
understand their limits and capabilities. With the rise of neuromorphic
hardware, it is even more critical to understand how a neural network, as a
distributed system, tolerates the failures of its computing nodes, neurons, and
its communication channels, synapses. Experimentally assessing the robustness
of neural networks involves the quixotic venture of testing all the possible
failures, on all the possible inputs, which ultimately hits a combinatorial
explosion for the first, and the impossibility to gather all the possible
inputs for the second.
In this paper, we prove an upper bound on the expected error of the output
when a subset of neurons crashes. This bound involves dependencies on the
network parameters that can be seen as being too pessimistic in the average
case. It involves a polynomial dependency on the Lipschitz coefficient of the
neurons activation function, and an exponential dependency on the depth of the
layer where a failure occurs. We back up our theoretical results with
experiments illustrating the extent to which our prediction matches the
dependencies between the network parameters and robustness. Our results show
that the robustness of neural networks to the average crash can be estimated
without the need to neither test the network on all failure configurations, nor
access the training set used to train the network, both of which are
practically impossible requirements.Comment: 36th IEEE International Symposium on Reliable Distributed Systems 26
- 29 September 2017. Hong Kong, Chin
Time-Varying Quantiles
A time-varying quantile can be fitted to a sequence of observations by formulating a time series model for the corresponding population quantile and iteratively applying a suitably modified state space signal extraction algorithm. Quantiles estimated in this way provide information on various aspects of a time series, including dispersion,
asymmetry and, for financial applications, value at risk. Tests for the constancy of quantiles, and associated contrasts, are constructed using indicator variables; these tests have a similar form to stationarity tests and, under the null hypothesis, their asymptotic distributions belong to the Cramér von Mises family. Estimates of the quantiles at the end of the series provide the basis for forecasting. As such they offer an alternative to conditional quantile autoregressions and, at the same time, give some insight into their structure and potential drawbacks
On the Properties of Simulation-based Estimators in High Dimensions
Considering the increasing size of available data, the need for statistical
methods that control the finite sample bias is growing. This is mainly due to
the frequent settings where the number of variables is large and allowed to
increase with the sample size bringing standard inferential procedures to incur
significant loss in terms of performance. Moreover, the complexity of
statistical models is also increasing thereby entailing important computational
challenges in constructing new estimators or in implementing classical ones. A
trade-off between numerical complexity and statistical properties is often
accepted. However, numerically efficient estimators that are altogether
unbiased, consistent and asymptotically normal in high dimensional problems
would generally be ideal. In this paper, we set a general framework from which
such estimators can easily be derived for wide classes of models. This
framework is based on the concepts that underlie simulation-based estimation
methods such as indirect inference. The approach allows various extensions
compared to previous results as it is adapted to possibly inconsistent
estimators and is applicable to discrete models and/or models with a large
number of parameters. We consider an algorithm, namely the Iterative Bootstrap
(IB), to efficiently compute simulation-based estimators by showing its
convergence properties. Within this framework we also prove the properties of
simulation-based estimators, more specifically the unbiasedness, consistency
and asymptotic normality when the number of parameters is allowed to increase
with the sample size. Therefore, an important implication of the proposed
approach is that it allows to obtain unbiased estimators in finite samples.
Finally, we study this approach when applied to three common models, namely
logistic regression, negative binomial regression and lasso regression
Robustness analysis of a Maximum Correntropy framework for linear regression
In this paper we formulate a solution of the robust linear regression problem
in a general framework of correntropy maximization. Our formulation yields a
unified class of estimators which includes the Gaussian and Laplacian
kernel-based correntropy estimators as special cases. An analysis of the
robustness properties is then provided. The analysis includes a quantitative
characterization of the informativity degree of the regression which is
appropriate for studying the stability of the estimator. Using this tool, a
sufficient condition is expressed under which the parametric estimation error
is shown to be bounded. Explicit expression of the bound is given and
discussion on its numerical computation is supplied. For illustration purpose,
two special cases are numerically studied.Comment: 10 pages, 5 figures, To appear in Automatic
BANDWIDTH SELECTION FOR SPATIAL HAC AND OTHER ROBUST COVARIANCE ESTIMATORS
This research note documents estimation procedures and results for an empirical investigation of the performance of the recently developed spatial, heteroskedasticity and autocorrelation consistent (HAC) covariance estimator calibrated with different kernel bandwidths. The empirical example is concerned with a hedonic price model for residential property values. The first bandwidth approach varies an a priori determined plug-in bandwidth criterion. The second method is a data driven cross-validation approach to determine the optimal neighborhood. The third approach uses a robust semivariogram to determine the range over which residuals are spatially correlated. Inference becomes more conservative as the plug-in bandwidth is increased. The data-driven approaches prove valuable because they are capable of identifying the optimal spatial range, which can subsequently be used to inform the choice of an appropriate bandwidth value. In our empirical example, pertaining to a standard spatial model and ditto dataset, the results of the data driven procedures can only be reconciled with relatively high plug-in values (n0.65 or n0.75). The results for the semivariogram and the cross-validation approaches are very similar which, given its computational simplicity, gives the semivariogram approach an edge over the more flexible cross-validation approach.spatial HAC, semivariogram, bandwidth, hedonic model
A Provable Smoothing Approach for High Dimensional Generalized Regression with Applications in Genomics
In many applications, linear models fit the data poorly. This article studies
an appealing alternative, the generalized regression model. This model only
assumes that there exists an unknown monotonically increasing link function
connecting the response to a single index of explanatory
variables . The generalized regression model is flexible and
covers many widely used statistical models. It fits the data generating
mechanisms well in many real problems, which makes it useful in a variety of
applications where regression models are regularly employed. In low dimensions,
rank-based M-estimators are recommended to deal with the generalized regression
model, giving root- consistent estimators of . Applications of
these estimators to high dimensional data, however, are questionable. This
article studies, both theoretically and practically, a simple yet powerful
smoothing approach to handle the high dimensional generalized regression model.
Theoretically, a family of smoothing functions is provided, and the amount of
smoothing necessary for efficient inference is carefully calculated.
Practically, our study is motivated by an important and challenging scientific
problem: decoding gene regulation by predicting transcription factors that bind
to cis-regulatory elements. Applying our proposed method to this problem shows
substantial improvement over the state-of-the-art alternative in real data.Comment: 53 page
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