Recent content by newphysist

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    Graduate Particle Swarm Optimization vs. Newton's Method

    I have been reading Stephen Boyd's book Convex Optimization and I have learned to form various problems like LP, QP, QCQP, SOCP or SDPs. I also learned about formulating SVM for classification problem as optimization problem. Now I am reading about Gradient Methods, Newton's method, etc...
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    Graduate Why Does L1 Regularization Lead to Sparse Solutions Unlike L2?

    I am trying to understand the difference between L1 vs. L2 regularization in OLS. I understand the concept of center of ellipsoid being the optimal solution and ellipse itself being contours of constant squared errors. And when we use L2 regularization we introduce a spherical constraint on...
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    Undergrad Angle between vector and its transpose

    Can you please explain what you mean by above projection example or did you switch v and w? I don't see any use of w in your logic. Thanks
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    Graduate Question from Boyd's Optimization Book

    Hi, I am reading Convex Optimization from Stephen Boyd's book on my own and I am stuck at math he mentions on Pg. 157 of his book which can be found here. How does he write the following: sup{uTP^{T}_{i}x | ||u||2 ≤ 1} = ||P^{T}_{i}x||2 Thanks guys
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    High School Multiplying a vector with Square Matrix vs. its transpose

    Hi, I am new to Math so I am trying to get some intuition. Let's say I have a matrix A of n x n and a vector B of n x 1 what is the difference between A x B and A' x B? Thanks
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    Undergrad Angle between vector and its transpose

    Assuming that question is meaningless, what is the intuition behind taking transpose?
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    Undergrad Angle between vector and its transpose

    Hi What is the angle between a vector (e.g. a row vector A) and it's transpose (a column vector) ? I know what transpose means mathematically but what is the intuition? Thanks guys
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    Undergrad Convexity of a function I don't understand

    Hi, I am starting to learn real math I would say for first time in life. I have come across this function: f(x) = maxi(xi) - mini(xi) The domain is R. Does the above function mean f(x) = 0 since for for x in R max and min of x would be x itself. Hence it is convex as for any...
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    Graduate What makes a function quasi-linear?

    Real numbers R
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    Graduate What makes a function quasi-linear?

    Hi, I have two questions. (1) I am trying to understand how the following function is quasi-linear: f = min(1/2,x,x^2) For it to be quasi linear it has to be quasi convex and quasi concave at same time. (2) I think the reason the above function is not concave is cause on a...
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    High School Is Autocorrelation of White Noise Zero?

    I am really new to this and so I am trying to understand some basic stuff here. Autocorrelation of a univariate white noise is 0. Am I correct?