Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Regression Toward the Mean01:52

Regression Toward the Mean

7.0K
Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
7.0K
Probability Laws01:49

Probability Laws

44.2K
Overview
44.2K
Real Zeros of Polynomials01:27

Real Zeros of Polynomials

188
Polynomials are algebraic expressions of terms with variables raised to non-negative integer powers. A central aspect of analyzing polynomial functions is determining their real zeros—values of the variable for which the polynomial evaluates to zero. These values represent the x-intercepts of the polynomial’s graph.The Rational Zeros Theorem lists possible rational solutions for a polynomial equation with integer coefficients. If f(x)=anxn+....+a0​, then every rational zero is...
188
Long Division of Polynomials01:26

Long Division of Polynomials

347
Polynomial division is an essential algebraic process to simplify expressions and solve equations. Just as numerical division separates a number into quotient and remainder, polynomial long division partitions a polynomial into simpler components; in this context, the dividend is the polynomial being divided, the divisor is the expression dividing it, and the result is expressed in terms of a quotient and a remainder.The division begins by arranging the dividend and divisor in standard...
347
Introduction to Polynomial Functions01:26

Introduction to Polynomial Functions

272
Polynomial functions are fundamental elements in algebra and calculus, defined by expressions that combine variables and constants through addition, subtraction, and multiplication, with the variable raised to nonnegative integer exponents. A general polynomial function of degree n is given byWhere an ≠ 0. The term anxn is the leading term, and an is the leading coefficient, while a0 is referred to as the constant term.Characteristics and ClassificationPolynomials are categorized by their...
272
Synthetic Disvision of Polynomials01:28

Synthetic Disvision of Polynomials

173
Synthetic division is an efficient algorithmic approach for dividing a polynomial by a linear binomial of the form x - c, where c is a real number. This method is helpful due to its streamlined process, which avoids the more cumbersome steps involved in the traditional long division of polynomials. It simplifies computation and serves as a practical tool for evaluating polynomials and identifying their factors.To perform synthetic division, one begins by listing the coefficients of the...
173

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Preformer MOT: A transformer-based approach for multi-object tracking with global trajectory prediction.

Fundamental research·2026
Same author

Fully-Distributed Neural-Network-Based Approaches for Monotonic Game With Finite-Time Disturbance Rejection.

IEEE transactions on cybernetics·2025
Same author

Is the Effect of Intensive Antihypertensive Treatment in Acute Intracerebral Hemorrhage Dependent on Hematoma Volume? A Traditional Meta-analysis of the Effect of Antihypertensive Regimens, a Bayesian Network Meta-analysis of the Mortality of Antihypertensive Drugs and Systematic Review.

CNS drugs·2025
Same author

Impacts of Statin Therapy Strategies on Incidence of Ischemic Cerebrovascular Events in Patients With Aneurysmal Subarachnoid Hemorrhage: A Systematic Review and Bayesian Network Meta-Analysis.

Neurosurgery·2023
Same author

Disulfiram in glioma: Literature review of drug repurposing.

Frontiers in pharmacology·2022
Same author

Short-Term Nationwide Airport Throughput Prediction With Graph Attention Recurrent Neural Network.

Frontiers in artificial intelligence·2022
Same journal

Relation DETR+: Exploring Explicit Position Relation Prior for Dense Prediction.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

RBF++: Quantifying and Optimizing Reasoning Boundaries across Measurable and Unmeasurable Capabilities for Chain-of-Thought Reasoning.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

CAFE: Cross-View Adaptive Fusion and Cluster Center Enhancement for Robust Multi-View Clustering.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

DIVER: Reinforced Diffusion Breaks Imitation Bottlenecks in End-to-End Autonomous Driving.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Ethics-Aware Safe Reinforcement Learning for Rare-Event Risk Control in Interactive Urban Driving.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Learning Shape Anchors for Holistic Indoor Scene Understanding.

IEEE transactions on pattern analysis and machine intelligence·2026
See all related articles

Related Experiment Video

Updated: Jan 30, 2026

Establishing a Competing Risk Regression Nomogram Model for Survival Data
04:57

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Published on: October 23, 2020

10.9K

Calibrating Classification Probabilities with Shape-Restricted Polynomial Regression.

Yongqiao Wang, Lishuai Li, Chuangyin Dang

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |February 1, 2019
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel probability calibration method using shape-restricted polynomial regression. It addresses limitations of existing techniques, ensuring flexibility, non-decreasingness, continuity, and tractability for accurate membership probability predictions.

    More Related Videos

    Solid Plate-based Dietary Restriction in Caenorhabditis elegans
    06:13

    Solid Plate-based Dietary Restriction in Caenorhabditis elegans

    Published on: May 28, 2011

    17.1K
    Assessment of Open Probability of the Mitochondrial Permeability Transition Pore in the Setting of Coenzyme Q Excess
    07:35

    Assessment of Open Probability of the Mitochondrial Permeability Transition Pore in the Setting of Coenzyme Q Excess

    Published on: June 1, 2022

    2.6K

    Related Experiment Videos

    Last Updated: Jan 30, 2026

    Establishing a Competing Risk Regression Nomogram Model for Survival Data
    04:57

    Establishing a Competing Risk Regression Nomogram Model for Survival Data

    Published on: October 23, 2020

    10.9K
    Solid Plate-based Dietary Restriction in Caenorhabditis elegans
    06:13

    Solid Plate-based Dietary Restriction in Caenorhabditis elegans

    Published on: May 28, 2011

    17.1K
    Assessment of Open Probability of the Mitochondrial Permeability Transition Pore in the Setting of Coenzyme Q Excess
    07:35

    Assessment of Open Probability of the Mitochondrial Permeability Transition Pore in the Setting of Coenzyme Q Excess

    Published on: June 1, 2022

    2.6K

    Area of Science:

    • Machine Learning
    • Statistical Modeling

    Background:

    • Accurate membership probability prediction is crucial for classification tasks.
    • Probability calibration aims to map classifier scores to reliable probabilities.
    • Existing methods struggle with universal flexibility, non-decreasingness, continuity, and computational tractability.

    Purpose of the Study:

    • To develop a computationally tractable probability calibration method satisfying four key desiderata.
    • To improve the accuracy and reliability of membership probability predictions in classification.

    Main Methods:

    • Utilized shape-restricted polynomial regression to approximate the calibrating function.
    • Employed monotone polynomials with semidefinite constraints to ensure non-decreasingness.
    • Formulated the calibration problem as a tractable semidefinite program.

    Main Results:

    • The proposed method achieves universal flexibility, non-decreasingness, continuity, and computational tractability.
    • The estimator demonstrates strong and weak universal consistency.
    • Experimental results show significant improvements in reliability-curve related measures.

    Conclusions:

    • Shape-restricted polynomial regression offers a viable solution for probability calibration.
    • The method enhances the performance and trustworthiness of classification models.
    • This approach advances the field of probability calibration in machine learning.