Questions tagged [linear-algebra]

A field of mathematics concerned with the study of finite dimensional vector spaces, including matrices and their manipulation, which are important in statistics.

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Finding linear transformation under which distance matrices are similar

I have n sets of vectors, where each set S_i contains k vectors in ...
4
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1answer
60 views

How do we define a linearly separable problem?

When we talk about Perceptrons, we say that they are limited for approximating functions that are linearly separable, while Neural Networks that use non-linear transformations are not. I am having ...
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20 views

Possible flaw in the MDS method for dimensionality reduction

The MDS (multidimensional scaling) method is used to solve the problem of dimensionality reduction. Basically, it does the following: given $n$ points $x_1,\cdots,x_n\in\mathbb R^d$, try to find a ...
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56 views

Linear algebra library for c++

I have been trying to find the substitute of numpy and perform some linear algebra using c++ and here's a list of libraries I have encountered: Eigen Armadillo Dlib GNU Scientific library Please ...
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49 views

How does SVD actually provide the recommendations? I seem to get conflicting answers

I am reading a text book that basically says the following: Given a matrix A where A is USERS x ITEMS we can use SVD to decompose the matrix into: $$A = U \times \Sigma \times V^T$$ Then we can take ...
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0answers
10 views

How effective is Moore Penrose for solving regression problems with overdetermined system of equations?

For regression problems with #Predictors > #observations, I recently read about Moore Penrose (pseudo inverse method) which solves the problem of non invertible matrix in OLS for regression problems. ...
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19 views

How to add extra constraints to an equation?

Background: I have an equation which looks like as follows: $W \times P = R$ $\left[\begin{array} &{1}&{0}&{0}&-\frac{w_{1}}{w_{o1}} &\dots &{0} &-\frac{w_{1}}{w_{0} } \\...
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0answers
156 views

Connection between piecewise linear basis functions and RELU activation function

ReLU activation is defined as follows $$\sigma(x)=\max(0, x).$$ Let's assume that I have deep network of 1 hidden layer, than output from my layer has form $$ f(x)= \sigma(Wx +b), $$ where matrix W ...
1
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0answers
74 views

Can we think of neurons as maps between matrices?

Usually when we think about neurons, we imagine that they enact some kind of map between real numbers. For example, a neuron might take in real numbers $x_{i}$ and weight them with parameters $W_{ij}$,...
1
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0answers
13 views

Structures for incorporating linear functions into a nonlinear optimization problem

I'm working on a problem which naturally involves both linear and nonlinear operations, and I'd like some help understanding the best way to combine these into a neural network framework. To be more ...
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28 views

How do I get confidence intervals for an ElasticNet in sklearn?

I need to produce a row for the confidence interval for every field that I am calculating coefficients and scores off of. So here is my code so far- ...
0
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1answer
218 views

Gradient descent formula implementation in python

So I recently started with Andrew Ng's ML Course and this is the formula that Andrew lays out for calculating gradient descent on a linear model. $$ \theta_j = \theta_j - \alpha \frac{1}{m} \sum_{i=1}...
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15 views

What does sparsely compute mean?

I heard someone say a neural network needs to sparsely compute the output. I get what compute means, I get what a sparse matrix is, but what does sparsely compute mean?
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17 views

Chaining bias terms in backprob

let's say I have a few linear layers $l_1 \dots l_n$: $y=I(\dots I(IX + b_1) + b_2) \dots +b_n)$ where $n$ is sufficiently large and $I$ is the (nonparametric) identity matrix. The gradient for $b_n$...
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10 views

Performant alternatives to Matrix package in R that requires minimal effort by end users to install

Background I'm going to be releasing a package for R that does calculations involving extremely large sparse matrices (1,000,000 x 1,000,000 is the minimum for what we consider useful). For this ...
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1answer
37 views

Can I use regression to solve a multiple equation problem

I'm working on a problem which is a multiple equation. I have a group of people and each person in the group is working on different tasks (e.g. n tasks in total). Each person in this group is working ...