Gilles R. Ducharme

A similarity measure to assess the stability of classification trees

It has been recognized that Classification trees (CART) are unstable; a small perturbation in the input variables or a fresh sample can lead to a very different classification tree. Some approaches exist that try to correct this instability. However, their benefits can, at present, be appreciated only qualitatively. A similarity measure between two classification trees is introduced that can measure their closeness. Its usefulness is illustrated with synthetic data on the impact of radioactivity deposit through the environment. In this context, a modified node level stabilizing technique, referred to as the NLS-REP method, is introduced and shown to be more stable than the classical CART method.

REFERENCE VALUES OBTAINED BY KERNEL-BASED ESTIMATION OF QUANTILE REGRESSIONS

In this paper, we study the problem of estimating non-parametrically a quantile regression curve as it applies to computing reference values. We propose an automatic procedure that uses a symmetrized nearest-neighbor kernel estimator of conditional distributions. We also discuss ways of measuring the dispersion of quantile regression estimator. One is based on the asymptotic distribution of such quantiles, while the other relies on the bootstrap method. The results of a small simulation study show that the methods of the paper perform rather well even in a situation where a good parametric solution is available. As an example, we analyze a small part of a data set that was collected to establish reference values for blood velocity in different parts of the umbilical cord of human fetuse as they grow toward birth.

Quasi Most Powerful Invariant Goodness-of-fit Tests

In this paper, we develop an approximation for the most powerful invariant test of one location-scale family against another one. The approach is based on the Laplace method for integrals and yields a very accurate approximation of the density of a maximal invariant. Moreover, it can be applied to a much wider set of pairs of densities than previously possible. Many examples are worked out. The resulting test is easy to compute and its power is shown to be very close to that of the best test. By using versions of the Laplace method, the approach is extended to goodness-of-fit tests for residuals in regression and to some multivariate distributions. A small simulation study confirms the theoretical results. An example concludes the paper. Copyright 2003 Board of the Foundation of the Scandinavian Journal of Statistics..

Goodness-of-fit tests for the inverse Gaussian and related distributions

In this paper, tests of goodness-of-fit for the inverse Gaussian distribution are developed. The distribution involves a shape parameter and, because of this, some test approaches lead to inconsistent strategies. A consistent test is proposed and its properties investigated. A table of critical points is provided and both the level and the power of the test are explored by simulation. It is seen that the test is more powerful than most of its competitors. The framework is widened to cover satellite distributions of the inverse Gaussian and some types of censored data. An example concludes the paper.

On Adaptive Bandwidth Selection for Efficient MIA

Recently, a generic DPA attack using the mutual information index as the side channel distinguisher has been introduced. Mutual Information Analysis’s (MIA) main interest is its claimed genericity. However, it requires the estimation of various probability density functions (PDF), which is a task that involves the complicated problem of selecting tuning parameters. This problem could be the cause of the lower efficiency of MIA that has been reported. In this paper, we introduce an approach that selects the tuning parameters with the goal of optimizing the performance of MIA. Our approach differs from previous works in that it maximizes the ability of MIA to discriminate one key among all guesses rather than optimizing the accuracy of PDF estimates. Application of this approach to various leakage traces confirms the soundness of our proposal.

Delay-correlation-aware SSTA based on conditional moments

Corner-based Timing Analysis (CTA) becomes more and more pessimistic as feature size shrinks. This trend has motivated the development of Statistical Static Timing Analysis (SSTA). In this paper, we propose a new path-based SSTA framework that allows the estimation of path delay distributions and delay correlations by propagating iteratively mean and variance of cell delay. These moments, conditioned on input slope and output load values, are pre-characterized by an improved method: log-logistic distribution based input signals and inverters as output load. In applications, the delay gains of this SSTA framework with respect to CTA are shown to be significant. It is also highlighted that the discrepancy of critical paths orderings obtained by SSTA and CTA depends on two factors: cell-to-cell delay correlation and standard deviation of cell delay.

Statistical cells timing metrics characterization

To characterize statistical moments of cell delays and slopes, the standard method is Monte Carlo (MC) method. However, this method suffers from very high computational cost. In this paper, we propose a technique to quickly and accurately estimate Standard Deviation (SD) of standard cell delays and slopes. The proposed technique is based on the identification, performed with a reduced set of MC simulations, of delay and output slope SD functions that take input slope, output load and supply voltage as input arguments. These identified functions are then used to estimate SDs of delays and slopes at different operating conditions (input slope, output load, supply voltage). This proposed method provides at least 76% of CPU gains, with respect to MC, while keeping high accuracy.

SSTA with delay correlations

Estimation of delay correlations is one of the most challenging problems in SSTA. This is because cell delay depends on a number of factors in a complex manner, which makes complex the estimation of correlations as well. In this paper, we introduce a technique to compute cell-to-cell and path-to-path delay correlations, which allows considering the effects of cell-level input/output edge, input slope and output lo ad values. Numerical results are presented to quantify its accuracy.

Interpreting SSTA results with correlation

Statistical Static Timing Analysis (SSTA) is becoming necessary; but has not been widely adopted. One of those arguments against the use is that results of SSTA are difficult to make use of for circuit design. In this paper, by introducing conditional moments, we propose a path-based statistical timing approach, which permits us to consider gate topology and switching process induced correlations. With the help of this gate-to-gate delay correlation, differences between results of SSTA and those of Worst-case Timing Analysis (WTA) are interpreted. Numerical results demonstrate that path delay means and standard deviations estimated by the proposed approach have absolute values of relative errors respectively less than 5% and 10%.

Mutual information analysis: higher-order statistical moments, efficiency and efficacy

The wide attention given to the mutual information analysis (MIA) is often connected to its statistical genericity, denoted flexibility in this paper. Indeed, MIA is expected to lead to successful key recoveries with no reliance on a priori knowledge about the implementation (impacted by the error modeling made by the attacker. and with as minimum assumptions as possible about the leakage distribution, i.e. able to exploit information lying in any statistical moment and to detect all types of functional dependencies), up to the error modeling which impacts its efficiency (and even its effectiveness). However, emphasis is put on the powerful generality of the concept behind the MIA, as well as on the significance of adequate probability density functions (PDF) estimation which seriously impacts its performance. By contrast to its theoretical advantages, MIA suffers from underperformance in practice limiting its usage. Considering that this underperformance could be explained by suboptimal estimation procedures, we studied in-depth MIA by analyzing the link between the setting of tuning parameters involved in the commonly used nonparametric density estimation, namely kernel density estimation, with respect to three criteria: the statistical moment where the leakage prevails, MIA’s efficiency and its flexibility according to the classical Hamming weight model. The goal of this paper was, therefore, to cast some interesting light on the field of PDF estimation issues in MIA for which much work has been devoted to finding improved estimators having their pros and cons, while little attempt has been made to identify whether existing classical methods can be practically improved or not according to the degree of freedom offered by hyperparameters (when available). We show that some ‘optimal’ estimation procedures following a problem-based approach rather than the systemic use of heuristics following an accuracy-based approach can make MIA more efficient and flexible and a practical guideline for tuning the hyperparameters involved in MIA should be designed. The results of this analysis allowed us defining a guideline based on a detailed comparison of MIA’s results across various simulations and real-world datasets (including publicly available ones such as DPA contest V2 and V4.1).