Wooseok HaOxford AcademicInformation and Inference: A Journal of the IMARina Foygel Barber and Wooseok Ha. Gradient descent with non-convex constraints: local concavity determines convergence. Information and Inference: A Journal of the IMA, 2018.
matrix-factorizationconstrained-optimizationdata-analysisrobust-optimizationgradient-descentmatlab-toolboxclustering-algorithmoptimization-algorithmsnmfonline-learningstochastic-optimizersnonnegativity-constraintsorthogonaldivergenceprobabilistic-matrix-factorizationnonnegative-matrix-factorizationsparse-representations ...
The second difference has to do with the cost function on which we apply the algorithm. Newton’s method has stronger constraints in terms of the differentiability of the function than gradient descent. If the second derivative of the function is undefined in the function’s root, then we can...
Conjugate gradient descent: A problem with gradient descent is that it may perform badly on certain types of functions. For example, if a function is steep and narrow, then gradient descent will take many very small steps to reach the minimum, bouncing back and forth, even if the function ...
This strategy reduces the error in gradient estimation compared to the conventional mini-batch stochastic gradient descent method. Our approach involves dividing the whole snapshot set into several Voronoi cells with low variance and extracting samples with good uniformity from each region to construct ...
Iterative procedures like stochastic gradient descent (SGD) [2], [3] and randomized Kaczmarz (RK) [4] method are often used for estimation of unknown parameters under such constraints. These methods sample a random row of the measurement matrix at each iteration and use it to estimate the ...
there is any non-uniformity in the sensitivity of the output\(\hat{X}\)to changes inXit must be due to the implicit constraints posed during learning. Analyzing the output sensitivity in this simple model will help to better understand the implicit preferences of learning with gradient descent....
2). It would also explain, in the case of kernel methods and square-loss regression, why the pseudoinverse solution provides good expected error and at the same time perfect interpolation on the training set12,13 with a data-dependent double-descent behavior. Fig. 1: Classical generalization ...
weeds of gradient descent without properly motivating why we would want to minimize a function. Outside of class, I’ve never run into a problem where there’s a single right answer that we’re solving for. Instead we’re trying to find a solution that satisfies some set of constraints. ...
Real-time Fixed-priorities Optimization Gradient descent 1. Introduction Real-time systems, which impose both functional and timing constraints, can be found in many mission-critical applications in domains such as automotive, aerospace and healthcare. These systems are usually composed of a set of ...