# 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 $\mathbb{R}^d$. I know there is some unknown linear transformation $W$ under which the distance matrix $D_i$ (a $k\times k$ ...
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### Intuition behind understanding eigenvectors and Machine Learning

I am struggling to understand linear algebra application in machine learning, and I am not able to answer the following question. Is the model learned in Machine Learning the eigenvector of the ...
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### Can all known ML algorithms be written as a sequence of matrix operations?

I keep hearing that machine learning is just linear algebra. Does that mean all known (and all possible?) ML algos, from random forest, to support-vector machines, to recursive neural networks, can ...
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### What are some theoretical approches to study Machine Learning/Deep Learning?

I've recently studied "basics of machine learning" (chapter 5) in Deep Learning by Ian Goodfellow. They're explaining ML with most of statistical and probabilitical methods. But I wish to ...
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### Projecting 3D Chemical Data Onto a 2D Plane in Motion

I'm trying to model the rotation of two hydrogen atoms about a carbon atom. Say I have a conceptual wheel on an axle that is attached to my car. The axle is described by two points in 3D space, as ...
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### Why transpose of independent feature matrix is necessary in case of linear regression?

I can follow classical linear regression steps: $Xw=y$ $X^{-1}Xw=X^{-1}y$ $Iw=X^{-1}y$ $w=X^{-1}y$ However, on implementing in Python, I see that instead of simply using ...
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### How does tensor product/multiplication work in TensorFlow?

In Tensorflow, I saw the following example: ...
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### What's wrong with my backpropagation through time (BTT) calculation or how to multiple a scaled vector and a matrix without matching dimensions?

I am trying to make a pretty simple RNN from scracth, using only Numpy library of Python. At this moment I am having troubles with BTT as I do not know how to proceed with situation when a ...
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### Workng of LME model used for a set of category variable(s) and a continuous variable?

LME models are being used to analyze the effect of continuos data and category data. Is this model appropriate for checking the effect of two independent variables - one with continuous values and ...
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### 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 ...
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### How to incorporate the uncertainty of the model coefficients in the prediction interval of a multiple linear regression

I'm dealing with the modeling of small experimental data sets. As most experimental work does not generate thousands of samples, but rather a handful, I need to be inventive in how to deal with this ...
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### 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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### 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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### 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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### optimizing a linear optimization function with linear constarints and binary variables

I am new to optimizations and trying to solve a problem, which I feel falls in the umbrella of optimization. I have an ojective function that needs to be maximized ...
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### 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 $W_{ij}$,...
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### 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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### Machine learning PhD Interview technical questions [closed]

I'm Software Engineer who applied to grad school for Machine Learning/Computer Vision PhD and currently waiting for interview calls. I'm brushing up Linear algebra/ ML topics. What kind of technical ...
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### How can I implement tangent distance for k-nearest neighbor in python/scikit-learn?

My ultimate aim is to have a function which I can feed into scikit-learn's NearestNeighbor class as a custom metric parameter. ...
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### Statistics Before Linear Algebra?

I know this is an opinion-based question and will be closed but this is the only place I know that can answer it reasonably and it is a very important matter to me. I am pursuing a machine ...
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