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Proofs you probably weren't taught

Proofs you probably weren't taught. Thursday, October 27, 2011. Proof for the first-order condition of convexity. We want to prove that. A function f(x), which is differentiable, is convex if and only if its domain is a convex set and if the following inequality condition is satisfied:. Intuitively, this condition says that the tangent/first-order-taylor-series approximation is globally an under-estimator of f(x). Definition of a convex function:. Where we have used the fact that g(0) = f(x). That the in...

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Proofs you probably weren't taught | mathgotchas.blogspot.com Reviews

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Proofs you probably weren't taught. Thursday, October 27, 2011. Proof for the first-order condition of convexity. We want to prove that. A function f(x), which is differentiable, is convex if and only if its domain is a convex set and if the following inequality condition is satisfied:. Intuitively, this condition says that the tangent/first-order-taylor-series approximation is globally an under-estimator of f(x). Definition of a convex function:. Where we have used the fact that g(0) = f(x). That the in...

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Proofs you probably weren't taught | mathgotchas.blogspot.com Reviews

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Proofs you probably weren't taught. Thursday, October 27, 2011. Proof for the first-order condition of convexity. We want to prove that. A function f(x), which is differentiable, is convex if and only if its domain is a convex set and if the following inequality condition is satisfied:. Intuitively, this condition says that the tangent/first-order-taylor-series approximation is globally an under-estimator of f(x). Definition of a convex function:. Where we have used the fact that g(0) = f(x). That the in...

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Proofs you probably weren't taught: July 2011

http://www.mathgotchas.blogspot.com/2011_07_01_archive.html

Proofs you probably weren't taught. Friday, July 22, 2011. Variational Calculus: What is the Shortest Distance Curve Connecting Two Points in 2D? Is it the straight line joining them? If so, why? Shortest Distance Curve Connecting Two Points. Posted by Deepak Roy Chittajallu. Labels: Shortest Distance Curve Connecting Two Points. Wednesday, July 20, 2011. Fermat' Theorem on Stationary Points - Why should the derivative vanish at Local/Global Extrema? Fermats Theorem Maxima Minima. Labels: Area of Circle.

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Proofs you probably weren't taught: June 2011

http://www.mathgotchas.blogspot.com/2011_06_01_archive.html

Proofs you probably weren't taught. Saturday, June 25, 2011. Principal Component Analysis (PCA) Demystified. Dimensionality reduction using PCA is typically taught using a cooking recipe such as the following:. Have you ever wondered where this recipe originated from. Below is the underlying proof in detail:. Posted by Deepak Roy Chittajallu. Labels: Principal Component Analysis (PCA). Why is integral of normal distribution = 1? Where does the mysterious normalizing constant come from?

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Proofs you probably weren't taught: Why is the error function minimized in logistic regression convex?

http://www.mathgotchas.blogspot.com/2011/10/why-is-error-function-minimized-in.html

Proofs you probably weren't taught. Friday, October 21, 2011. Why is the error function minimized in logistic regression convex? We want to prove that the error/objective function of logistic regression :. Before beginning the proof, i would first like to make you review/recollect a few definitions/rules/facts/results related to convex functions:. Definition of a convex function:. A function f(x) is said to be convex if the following inequality holds true:. First-order condition of convexity:. Is a conve...

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Proofs you probably weren't taught: Variational Calculus: What is the Shortest Distance Curve Connecting Two Points in 2D? Is it the straight line joining them? If so, why?

http://www.mathgotchas.blogspot.com/2011/07/what-is-shortest-distance-curve.html

Proofs you probably weren't taught. Friday, July 22, 2011. Variational Calculus: What is the Shortest Distance Curve Connecting Two Points in 2D? Is it the straight line joining them? If so, why? Shortest Distance Curve Connecting Two Points. Posted by Deepak Roy Chittajallu. Labels: Shortest Distance Curve Connecting Two Points. Subscribe to: Post Comments (Atom). Curiosity is the mother of all invention! View my complete profile. Circumference of a Circle. Fermats Thoerem on Stationary Points.

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Proofs you probably weren't taught: Principal Component Analysis (PCA) Demystified

http://www.mathgotchas.blogspot.com/2011/06/principal-component-analysis-pca.html

Proofs you probably weren't taught. Saturday, June 25, 2011. Principal Component Analysis (PCA) Demystified. Dimensionality reduction using PCA is typically taught using a cooking recipe such as the following:. Have you ever wondered where this recipe originated from. Below is the underlying proof in detail:. Posted by Deepak Roy Chittajallu. Labels: Principal Component Analysis (PCA). Subscribe to: Post Comments (Atom). Curiosity is the mother of all invention! View my complete profile.

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Homepage of Deepak Roy Chittajallu

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Homepage of Deepak Roy Chittajallu. S Florian, R. Kohler, Y. Iwamoto, J.D. Orth, R. Weissleder, G. Danuser, and T. Mitchison,"In vivo cell-cycle profiling in xenograft tumors by quantitative intravital microscopy", Nature methods (2015). N Paragios, and I.A. Kakadiaris, An explicit shape-constrained MRF-based contour evolution method for 2D Medical Image Segmentation, IEEE Journal of Biomedical and Health Informatics (formerly IEEE TITB), 18(1):120-129, April, 2013. U Kurkure, D.R. Chittajallu. S Shah, I...

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Homepage of Deepak Roy Chittajallu

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Homepage of Deepak Roy Chittajallu. Welcome to my homepage. I am currently working as an R&D Engineer in the medical computing team of Kitware. Prior to which i did my Postdoctoral Training in Harvard Medical School. Under the supervision of Prof. Gaudenz Danuser. Prior to joining Harvard University, I did a Ph.D. and M.Sc. in Computer Science from University of Houston. Under the supervision of Prof. Ioannis A. Kakadiaris.

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Homepage of Deepak Roy Chittajallu

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Homepage of Deepak Roy Chittajallu. Computer Vision, Image Analysis, Machine Learning, Data Mining, Pattern Classificaiton, Pattern Recognition, Computer-Aided Diagnosis, Discrete and Convex Optimization, Graphical Models, Markov Random Field Models. Postdoctoral Training in Computational Biology. Harvard University, Cambridge, MA, USA. PhD in Computer Science. University Of Houston, Houston, Texas, USA. Prof Ioannis A. Kakadiaris. MSc in Computer Science. Department of Computer Science. Carrboro, NC, USA.

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Proofs you probably weren't taught

Proofs you probably weren't taught. Thursday, October 27, 2011. Proof for the first-order condition of convexity. We want to prove that. A function f(x), which is differentiable, is convex if and only if its domain is a convex set and if the following inequality condition is satisfied:. Intuitively, this condition says that the tangent/first-order-taylor-series approximation is globally an under-estimator of f(x). Definition of a convex function:. Where we have used the fact that g(0) = f(x). That the in...

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