arXiv subjects

Fadhel Ayed

Publications and source records attributed to Fadhel Ayed.

29 records · Page 2Linked to original sources

arXiv2023

A Framework for the Evaluation of Network Reliability Under Periodic Demand

In this paper, we study network reliability in relation to a periodic time-dependent utility function that reflects the system's functional performance. When an anomaly occurs, the system incurs a loss of utility that depends on the anomaly's timing and duration. We analyze the long-term average utility loss by considering exponential anomalies' inter-arrival times and general distributions of maintenance duration. We show that the expected utility loss converges in probability to a simple form. We then extend our convergence results to more general distributions of anomalies' inter-arrival times and to particular families of non-periodic utility functions. To validate our results, we use data gathered from a cellular network consisting of 660 base stations and serving over 20k users. We demonstrate the quasi-periodic nature of users' traffic and the exponential distribution of the anomalies' inter-arrival times, allowing us to apply our results and provide reliability scores for the network. We also discuss the convergence speed of the long-term average utility loss, the interplay between the different network's parameters, and the impact of non-stationarity on our convergence results.

cs.IT↗

arXiv2023

Accordion: A Communication-Aware Machine Learning Framework for Next Generation Networks

In this article, we advocate for the design of ad hoc artificial intelligence (AI)/machine learning (ML) models to facilitate their usage in future smart infrastructures based on communication networks. To motivate this, we first review key operations identified by the 3GPP for transferring AI/ML models through 5G networks and the main existing techniques to reduce their communication overheads. We also present a novel communication-aware ML framework, which we refer to as Accordion, that enables an efficient AI/ML model transfer thanks to an overhauled model training and communication protocol. We demonstrate the communication-related benefits of Accordion, analyse key performance trade-offs, and discuss potential research directions within this realm.

cs.NI↗

arXiv2022

The Normal-Generalised Gamma-Pareto process: A novel pure-jump Lévy process with flexible tail and jump-activity properties

Pure-jump Lévy processes are popular classes of stochastic processes which have found many applications in finance, statistics or machine learning. In this paper, we propose a novel family of self-decomposable Lévy processes where one can control separately the tail behavior and the jump activity of the process, via two different parameters. Crucially, we show that one can sample exactly increments of this process, at any time scale; this allows the implementation of likelihood-free Markov chain Monte Carlo algorithms for (asymptotically) exact posterior inference. We use this novel process in Lévy-based stochastic volatility models to predict the returns of stock market data, and show that the proposed class of models leads to superior predictive performances compared to classical alternatives.

stat.ME↗

arXiv2021

Regularization in ResNet with Stochastic Depth

Regularization plays a major role in modern deep learning. From classic techniques such as L1,L2 penalties to other noise-based methods such as Dropout, regularization often yields better generalization properties by avoiding overfitting. Recently, Stochastic Depth (SD) has emerged as an alternative regularization technique for residual neural networks (ResNets) and has proven to boost the performance of ResNet on many tasks [Huang et al., 2016]. Despite the recent success of SD, little is known about this technique from a theoretical perspective. This paper provides a hybrid analysis combining perturbation analysis and signal propagation to shed light on different regularization effects of SD. Our analysis allows us to derive principled guidelines for choosing the survival rates used for training with SD.

stat.ML↗

arXiv2020

An Information Theoretic approach to Post Randomization Methods under Differential Privacy

Post Randomization Methods (PRAM) are among the most popular disclosure limitation techniques for both categorical and continuous data. In the categorical case, given a stochastic matrix $M$ and a specified variable, an individual belonging to category $i$ is changed to category $j$ with probability $M_{i,j}$. Every approach to choose the randomization matrix $M$ has to balance between two desiderata: 1) preserving as much statistical information from the raw data as possible; 2) guaranteeing the privacy of individuals in the dataset. This trade-off has generally been shown to be very challenging to solve. In this work, we use recent tools from the computer science literature and propose to choose $M$ as the solution of a constrained maximization problems. Specifically, $M$ is chosen as the solution of a constrained maximization problem, where we maximize the Mutual Information between raw and transformed data, given the constraint that the transformation satisfies the notion of Differential Privacy. For the general Categorical model, it is shown how this maximization problem reduces to a convex linear programming and can be therefore solved with known optimization algorithms.

stat.ME↗

arXiv2020

A Good-Turing estimator for feature allocation models

Feature allocation models generalize species sampling models by allowing every observation to belong to more than one species, now called features. Under the popular Bernoulli product model for feature allocation, given $n$ samples, we study the problem of estimating the missing mass $M_{n}$, namely the expected number hitherto unseen features that would be observed if one additional individual was sampled. This is motivated by numerous applied problems where the sampling procedure is expensive, in terms of time and/or financial resources allocated, and further samples can be only motivated by the possibility of recording new unobserved features. We introduce a simple, robust and theoretically sound nonparametric estimator $\hat{M}_{n}$ of $M_{n}$. $\hat{M}_{n}$ turns out to have the same analytic form of the popular Good-Turing estimator of the missing mass in species sampling models, with the difference that the two estimators have different ranges. We show that $\hat{M}_{n}$ admits a natural interpretation both as a jackknife estimator and as a nonparametric empirical Bayes estimator, we give provable guarantees for the performance of $\hat{M}_{n}$ in terms of minimax rate optimality, and we provide with an interesting connection between $\hat{M}_{n}$ and the Good-Turing estimator for species sampling. Finally, we derive non-asymptotic confidence intervals for $\hat{M}_{n}$, which are easily computable and do not rely on any asymptotic approximation. Our approach is illustrated with synthetic data and SNP data from the ENCODE sequencing genome project.

math.ST↗

arXiv2020

Anomaly Detection at Scale: The Case for Deep Distributional Time Series Models

This paper introduces a new methodology for detecting anomalies in time series data, with a primary application to monitoring the health of (micro-) services and cloud resources. The main novelty in our approach is that instead of modeling time series consisting of real values or vectors of real values, we model time series of probability distributions over real values (or vectors). This extension to time series of probability distributions allows the technique to be applied to the common scenario where the data is generated by requests coming in to a service, which is then aggregated at a fixed temporal frequency. Our method is amenable to streaming anomaly detection and scales to monitoring for anomalies on millions of time series. We show the superior accuracy of our method on synthetic and public real-world data. On the Yahoo Webscope data set, we outperform the state of the art in 3 out of 4 data sets and we show that we outperform popular open-source anomaly detection tools by up to 17% average improvement for a real-world data set.

cs.LG↗

arXiv2019

Beyond the Chinese Restaurant and Pitman-Yor processes: Statistical Models with Double Power-law Behavior

Bayesian nonparametric approaches, in particular the Pitman-Yor process and the associated two-parameter Chinese Restaurant process, have been successfully used in applications where the data exhibit a power-law behavior. Examples include natural language processing, natural images or networks. There is also growing empirical evidence that some datasets exhibit a two-regime power-law behavior: one regime for small frequencies, and a second regime, with a different exponent, for high frequencies. In this paper, we introduce a class of completely random measures which are doubly regularly-varying. Contrary to the Pitman-Yor process, we show that when completely random measures in this class are normalized to obtain random probability measures and associated random partitions, such partitions exhibit a double power-law behavior. We discuss in particular three models within this class: the beta prime process (Broderick et al. (2015, 2018), a novel process called generalized BFRY process, and a mixture construction. We derive efficient Markov chain Monte Carlo algorithms to estimate the parameters of these models. Finally, we show that the proposed models provide a better fit than the Pitman-Yor process on various datasets.

stat.ML↗

arXiv2019

Consistent estimation of the missing mass for feature models

Feature models are popular in machine learning and they have been recently used to solve many unsupervised learning problems. In these models every observation is endowed with a finite set of features, usually selected from an infinite collection $(F_{j})_{j\geq 1}$. Every observation can display feature $F_{j}$ with an unknown probability $p_{j}$. A statistical problem inherent to these models is how to estimate, given an initial sample, the conditional expected number of hitherto unseen features that will be displayed in a future observation. This problem is usually referred to as the missing mass problem. In this work we prove that, using a suitable multiplicative loss function and without imposing any assumptions on the parameters $p_{j}$, there does not exist any universally consistent estimator for the missing mass. In the second part of the paper, we focus on a special class of heavy-tailed probabilities $(p_{j})_{j\geq 1}$, which are common in many real applications, and we show that, within this restricted class of probabilities, the nonparametric estimator of the missing mass suggested by Ayed et al. (2017) is strongly consistent. As a byproduct result, we will derive concentration inequalities for the missing mass and the number of features observed with a specified frequency in a sample of size $n$.

math.ST↗

arXiv2019

Nonnegative Bayesian nonparametric factor models with completely random measures for community detection

We present a Bayesian nonparametric Poisson factorization model for modeling network data with an unknown and potentially growing number of overlapping communities. The construction is based on completely random measures and allows the number of communities to either increase with the number of nodes at a specified logarithmic or polynomial rate, or be bounded. We develop asymptotics for the number of nodes and the degree distribution of the network and derive a Markov chain Monte Carlo algorithm for targeting the exact posterior distribution for this model. The usefulness of the approach is illustrated on various real networks.

stat.ME↗

arXiv2018

On consistent estimation of the missing mass

Given $n$ samples from a population of individuals belonging to different types with unknown proportions, how do we estimate the probability of discovering a new type at the $(n+1)$-th draw? This is a classical problem in statistics, commonly referred to as the missing mass estimation problem. Recent results by Ohannessian and Dahleh \citet{Oha12} and Mossel and Ohannessian \citet{Mos15} showed: i) the impossibility of estimating (learning) the missing mass without imposing further structural assumptions on the type proportions; ii) the consistency of the Good-Turing estimator for the missing mass under the assumption that the tail of the type proportions decays to zero as a regularly varying function with parameter $α\in(0,1)$. In this paper we rely on tools from Bayesian nonparametrics to provide an alternative, and simpler, proof of the impossibility of a distribution-free estimation of the missing mass. Up to our knowledge, the use of Bayesian ideas to study large sample asymptotics for the missing mass is new, and it could be of independent interest. Still relying on Bayesian nonparametric tools, we then show that under regularly varying type proportions the convergence rate of the Good-Turing estimator is the best rate that any estimator can achieve, up to a slowly varying function, and that minimax rate must be at least $n^{-α/2}$. We conclude with a discussion of our results, and by conjecturing that the Good-Turing estimator is an rate optimal minimax estimator under regularly varying type proportions.

math.ST↗