Questions tagged [linear-algebra]

For questions about the use/aspects/implementation/intuition/mathematical proofs of various Linear Algebra methods used in Machine Learning and AI algorithms.

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Simplifying Log Loss

I am reading through a paper (https://www.mitpressjournals.org/doi/pdf/10.1162/0891201053630273) where they describe logloss as a ranking function and can be simplified to the margin of the training ...
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1answer
42 views

How do you find the homography matrix given 4 points in both images?

I want to understand the process of finding a homography matrix given 4 points in both images. I am able to do that in python OpenCV, but I wonder how it works behind the scenes. Suppose I have ...
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51 views

Is there any way to apply linear transformations on a vector other than matrix multiplication?

I am trying to optimize the cost function calculation in regression analysis using a non-matrix multiplication based approach. More specifically, I have a point $x = (1, 1, 2, 3)$, to which I want to ...
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55 views

Why MLP cannot approximate a closed shape function?

[TL;DR] I generated two classes Red and Blue on a 2D space. Red are points on Unit Circle and Blue are points on a Circle Ring with radius limits (3,4). I tried to train a Multi Layer Perceptron ...
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CSP Formulation of an algebraic problem

Is anyone able to explain how to do this? I'm not looking for the complete answer, I would settle for a "how to for dummies" explanation of how this is supposed to be solved. I understand ...
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0answers
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Estimating Baselines using ALS

I am trying to figure out how ALS works when minimizing the following formula: $\\ \\$ $\text{min}_{\lbrace b_u,b_i \rbrace} \sum_{(u,i)\in \mathcal{K}} (r_{ui} - \bar{r} - b_u - b_i )^2 + \lambda_{...
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1answer
211 views

What does it mean to do multi-dimensional processing with tensors in tensor cores?

In some tweets about NeurIPS 2018, this video from NVIDIA appeared. At around 0.37, she says: If you think about the current computations in our deep learning systems, they are all based on Linear ...
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1answer
151 views

Using reinforcement learning to find a preconditioner for linear systems of the form Ax = b

Sparse linear systems are normally solved by using solvers like MINRES, Conjugate gradient, GMRES. Efficient preconditioning, i.e., finding a matrix P such that PAx = Pb is easier to solve than the ...
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1answer
287 views

Does k consistency always imply (k - 1) consistency?

From Russell-Norvig: A CSP is strongly k-consistent if it is k-consistent and is also (k − 1)-consistent, (k − 2)-consistent, . . . all the way down to 1-consistent. How can a CSP be k-consistent ...
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338 views

How does neural network classifier classify from just drawing a decision plane?

I understand that a neural network basically distorts(non-linear transformation) and changes the perspective(linear transformations) of input space to draw a plane to classify data. How does the ...