Gradient descent-type methods: Background and simple unified convergence analysis

In this book chapter, we briefly describe the main components that constitute the gradient descent method and its accelerated and stochastic variants. We aim at explaining these components from a mathematical point of view, including theoretical and practical aspects, but at an elementary level. We will focus on basic variants of the gradient descent method and then extend our view to recent variants, especially variance-reduced stochastic gradient schemes (SGD). Our approach relies on revealing the structures presented inside the problem and the assumptions imposed on the objective function. Our convergence analysis unifies several known results and relies on a general, but elementary recursive expression. We have illustrated this analysis on several common schemes

A unified convergence analysis for shuffling-type gradient methods

In this paper, we propose a unified convergence analysis for a class of generic shuffling-type gradient methods for solving finite-sum optimization problems. Our analysis works with any sampling without replacement strategy and covers many known variants such as randomized reshuffling, deterministic or randomized single permutation, and cyclic and incremental gradient schemes. We focus on two different settings: strongly convex and nonconvex problems, but also discuss the non-strongly convex case. Our main contribution consists of new non-asymptotic and asymptotic convergence rates for a wide class of shuffling-type gradient methods in both nonconvex and convex settings. We also study uniformly randomized shuffling variants with different learning rates and model assumptions. While our rate in the nonconvex case is new and significantly improved over existing works under standard assumptions, the rate on the strongly convex one matches the existing best-known rates prior to this paper up to a constant factor without imposing a bounded gradient condition. Finally, we empirically illustrate our theoretical results via two numerical examples: nonconvex logistic regression and neural network training examples. As byproducts, our results suggest some appropriate choices for diminishing learning rates in certain shuffling variants

Faktor Penguat Pada Peningkatan Kinerja Karyawan PT. Gading Murni Surabaya

The purpose of this study is to determine which factors as an amplifier to improve the performance of employees of PT. Gading Murni Surabaya, between the leadership style and compensation received by employees. This study uses a survey approach by collecting data using a questionnaire of 50 respondents then analyzed using quantitative methods. The regession equation is Y = 8.009 + 0,223 X1 + 0,240 X2. The results of this study concluded that the leadership style and compensation variables had a corrected item total correlation value exceeding r table = 0.284 and the reliability test of the leadership style variable, and the alpha cronbach's compensation results exceeded 0.060, which means that the variable was valid and reliable. Leadership and compensation styles also simultaneously have a significant effect on employee performance. And the independent variable that has the largest beta coefficient is the compensation variable (X2) with a beta coefficient of 0.240.   Keywords : Leadership style, Compesation and Employee Performance

Global burden and strength of evidence for 88 risk factors in 204 countries and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

Background: Understanding the health consequences associated with exposure to risk factors is necessary to inform public health policy and practice. To systematically quantify the contributions of risk factor exposures to specific health outcomes, the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 aims to provide comprehensive estimates of exposure levels, relative health risks, and attributable burden of disease for 88 risk factors in 204 countries and territories and 811 subnational locations, from 1990 to 2021. Methods: The GBD 2021 risk factor analysis used data from 54 561 total distinct sources to produce epidemiological estimates for 88 risk factors and their associated health outcomes for a total of 631 risk–outcome pairs. Pairs were included on the basis of data-driven determination of a risk–outcome association. Age-sex-location-year-specific estimates were generated at global, regional, and national levels. Our approach followed the comparative risk assessment framework predicated on a causal web of hierarchically organised, potentially combinative, modifiable risks. Relative risks (RRs) of a given outcome occurring as a function of risk factor exposure were estimated separately for each risk–outcome pair, and summary exposure values (SEVs), representing risk-weighted exposure prevalence, and theoretical minimum risk exposure levels (TMRELs) were estimated for each risk factor. These estimates were used to calculate the population attributable fraction (PAF; ie, the proportional change in health risk that would occur if exposure to a risk factor were reduced to the TMREL). The product of PAFs and disease burden associated with a given outcome, measured in disability-adjusted life-years (DALYs), yielded measures of attributable burden (ie, the proportion of total disease burden attributable to a particular risk factor or combination of risk factors). Adjustments for mediation were applied to account for relationships involving risk factors that act indirectly on outcomes via intermediate risks. Attributable burden estimates were stratified by Socio-demographic Index (SDI) quintile and presented as counts, age-standardised rates, and rankings. To complement estimates of RR and attributable burden, newly developed burden of proof risk function (BPRF) methods were applied to yield supplementary, conservative interpretations of risk–outcome associations based on the consistency of underlying evidence, accounting for unexplained heterogeneity between input data from different studies. Estimates reported represent the mean value across 500 draws from the estimate's distribution, with 95% uncertainty intervals (UIs) calculated as the 2·5th and 97·5th percentile values across the draws. Findings: Among the specific risk factors analysed for this study, particulate matter air pollution was the leading contributor to the global disease burden in 2021, contributing 8·0% (95% UI 6·7–9·4) of total DALYs, followed by high systolic blood pressure (SBP; 7·8% [6·4–9·2]), smoking (5·7% [4·7–6·8]), low birthweight and short gestation (5·6% [4·8–6·3]), and high fasting plasma glucose (FPG; 5·4% [4·8–6·0]). For younger demographics (ie, those aged 0–4 years and 5–14 years), risks such as low birthweight and short gestation and unsafe water, sanitation, and handwashing (WaSH) were among the leading risk factors, while for older age groups, metabolic risks such as high SBP, high body-mass index (BMI), high FPG, and high LDL cholesterol had a greater impact. From 2000 to 2021, there was an observable shift in global health challenges, marked by a decline in the number of all-age DALYs broadly attributable to behavioural risks (decrease of 20·7% [13·9–27·7]) and environmental and occupational risks (decrease of 22·0% [15·5–28·8]), coupled with a 49·4% (42·3–56·9) increase in DALYs attributable to metabolic risks, all reflecting ageing populations and changing lifestyles on a global scale. Age-standardised global DALY rates attributable to high BMI and high FPG rose considerably (15·7% [9·9–21·7] for high BMI and 7·9% [3·3–12·9] for high FPG) over this period, with exposure to these risks increasing annually at rates of 1·8% (1·6–1·9) for high BMI and 1·3% (1·1–1·5) for high FPG. By contrast, the global risk-attributable burden and exposure to many other risk factors declined, notably for risks such as child growth failure and unsafe water source, with age-standardised attributable DALYs decreasing by 71·5% (64·4–78·8) for child growth failure and 66·3% (60·2–72·0) for unsafe water source. We separated risk factors into three groups according to trajectory over time: those with a decreasing attributable burden, due largely to declining risk exposure (eg, diet high in trans-fat and household air pollution) but also to proportionally smaller child and youth populations (eg, child and maternal malnutrition); those for which the burden increased moderately in spite of declining risk exposure, due largely to population ageing (eg, smoking); and those for which the burden increased considerably due to both increasing risk exposure and population ageing (eg, ambient particulate matter air pollution, high BMI, high FPG, and high SBP). Interpretation: Substantial progress has been made in reducing the global disease burden attributable to a range of risk factors, particularly those related to maternal and child health, WaSH, and household air pollution. Maintaining efforts to minimise the impact of these risk factors, especially in low SDI locations, is necessary to sustain progress. Successes in moderating the smoking-related burden by reducing risk exposure highlight the need to advance policies that reduce exposure to other leading risk factors such as ambient particulate matter air pollution and high SBP. Troubling increases in high FPG, high BMI, and other risk factors related to obesity and metabolic syndrome indicate an urgent need to identify and implement interventions

Gradient descent-type methods : Background and simple unified convergence analysis

In this book chapter, we briefly describe the main components that constitute the gradient descent method and its accelerated and stochastic variants. We aim at explaining these components from a mathematical point of view, including theoretical and practical aspects, but at an elementary level. We will focus on basic variants of the gradient descent method and then extend our view to recent variants, especially variance-reduced stochastic gradient schemes (SGD). Our approach relies on revealing the structures presented inside the problem and the assumptions imposed on the objective function. Our convergence analysis unifies several known results and relies on a general, but elementary recursive expression. We have illustrated this analysis on several common schemes

Confidence estimation of feedback information for logic diagnosis

International audienceThis paper proposes an estimation method for the confidence level of feedback information (CLFI), namely the confidence level of reported information in computer integrated manufacturing (CIM) architecture for logic diagnosis. This confidence estimation provides a diagnosis module with precise reported information to quickly identify the origin of equipment failure. We studied the factors affecting CLFI, such as measurement system reliability, production context, position of sensors in the acquisition chains, type of products, reference metrology, preventive maintenance and corrective maintenance based on historical data and feedback information generated by production equipments. We introduced the new 'CLFI' concept based on the Dynamic Bayesian Network approach and Tree Augmented Naïve Bayes model. Our contribution includes an on-line confidence computation module for production equipment data, and an algorithm to compute CLFI. We suggest it to be applied to the semiconductor manufacturing industry

Confidence of Reported Information for Real Time in Diagnosis of Complex Discrete Events Systems: A Semiconductor Application

International audienceNowadays, Semiconductor Manufacturing is operating in an intense competitive environment. These companies are developing manufacturing solutions to improve the quality of the process which improves the production equipment effectiveness. We can cite many different directions such as virtual metrology, dynamic control plan, and maintenance, etc. In this paper, we propose to contribute to an on-line diagnosis method helping human operator to identify equipments at the origin of a propagated failure. Our contribution consists in providing an on-line confidence calculating module of the data issued from the manufacturing equipments. Bayesian networks theory and Naïve algorithm are at the base of the proposed approach

Prise en compte des incertitudes sur les données de captage pour le diagnostic

Workshop: 4ème Workshop du Groupement d'Intérêt Scientifique "Surveillance, Sûreté et Sécurité des Grands Systèmes " (3SGS'11), Valenciennes, : France (2011)L'industrie du semi-conducteur est considérée comme particulièrement sensible aux aléas et aux contraintes de fonctionnement et la recherche permanente d'une production à capacité maximale est l'un des principaux objectifs de ce secteur, ceci afin d'assurer un retour sur investissement sur des machines très onéreuses. Parmi les incertitudes telles que celles liées au flux de produit, aux contaminations, aux opérateurs humains, à la cohabitation prototypage R&D et production, etc..., nous avons souhaité, dans le cadre de cette thèse, nous focaliser sur celles liées au système de captage du site de production. La contribution de nos travaux réside précisément dans la proposition d'une approche globale de diagnostic permettant de mener des inférences non seulement sur le calcul de la confiance qui peut être accordée aux informations issues du système de captage mais également des inférences permettant, lors de l'occurrence d'une défaillance détectée par une machine de métrologie de localiser, avec précision, la ou les machines à l'origine possible du défaut. L'approche générale retenue et l'originalité qui en découle revient à intégrer un raisonnement Bayésien au sein d'une approche de diagnostic logique. L'approche développée prend pour cadre d'étude un procédé industriel réel, les ateliers de production de semiconducteurs du projet Européen IMPROVE. L'approche vise ainsi à apporter des améliorations dans le traitement des défaillances et donc dans l'amélioration des performances de ces ateliers en permettant de réduire les temps de prise de décision (maintenances correctives). La suite des recherches va nous permettre dans un premier temps d'appliquer les premiers résultats obtenus sur des données concrètes. Dans un deuxième temps, nous nous proposons d'étendre le modèle Bayésien à ce jour retenu aux aspects dynamiques afin de tenir compte de l'impact de la chronologie des événements. Après quoi nous étendrons l'algorithme de diagnostic initialement proposé par M. Deschamps de manière à ce qu'il puisse intégrer le raisonnement Bayésien

Confidence Estimation of Feedback Information Using Dynamic Bayesian Networks

International audienceThis paper proposes an estimation method for the confidence level of feedback information (CLFI), namely the confidence level of reported information in computer integrated manufacturing (CIM) architecture for logic diagnosis. We studied the factors affecting CLFI, such as the measurement system reliability, production context, position of sensors in the acquisition chains, type of products, reference metrology, preventive maintenance and corrective maintenance based on historical data and feedback information generated by production equipments. We introduced the new 'CLFI' concept based on the Dynamic Bayesian Network(DBN) approach, Naïve Bayes model and Tree Augmented Naïve Bayes model. Our contribution includes an online confidence computation module for production equipments data and an algorithm to compute CLFI