# Questions tagged [tensor]

In machine learning, tensor is a multidimensional (multi-index, or multi-way) array of numbers, i.e. a generalization of a matrix.

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### How to leverage the separable functions in MCMC sampling? [closed]

I'm considering the posterior of a parametric model via the Bayesian approach. More specificity, I have a parametric model $u(p_1,p_2, p_3) = u_1(p_1) \times u_2(p_2) \times u_3(p_3)$ and I want to ...
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### Is the design matrix in a panel regression model a tensor?

In a panel regression model of the form $$Y_{it} = \mathbf{X}_{it} \pmb{\beta} + \epsilon_{it}$$ where $Y_{it}$ is the dependent variable for unit $i$ at time $t$ $\mathbf{X}_{it}$ is a vector of $K$ ...
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### Is spiked tensor decomposition a special case of INDSCAL decomposition?

I understand that "Spiked" often refers to the presence of a dominant component (or a few dominant components) in a tensor decomposition. Spiked tensor decomposition is applied to multi-way ...
71 views

### Transformers: Cross Attention Tensor Shapes During Inference Mode

Using the "classic" transformer model describing in "Attention is All You Need", I'm struggling to understand how the Encoder output is used by the Decoder during cross attention ...
49 views

### How do continuous partial derivatives depend on $n$ in maximum likelihood estimation?

I'm reading Tensor Methods in Statistics by McCullagh 1987, (P209 for this question) and I can't understand one step he uses. He begins with the usual log-likelihood \begin{equation*} l(\theta; Y) =...
343 views

Attention, as long as gradient calculations care, is two nested tensor multiplications and a softmax. I thought that, then, multi-head attention with $h=8$ and $d_k=64$ results in the same tensor with ...
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### How to adjust the scaling of the new data while use Incremental training of a neural network?

I am planning to use incremental training of my neural network model since I continually get new data and at present retrain the model after a period of time but the training window shifts forward. To ...
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### mgcv: Use of s() or te() with interactions in GAMs?

I am trying to model CO2 fluxes (fco2) using a number of environmental parameters using a GAM in mgcv. Specifically, I have leaf temperature (tl), vapour pressure deficit (vpd), and soil water content ...
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1 vote
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### Constaint on te() tensor product gam mgcv

In the mgcv package in R, I'm working on models whose covariates are forced to change shape at the median (=0). These are the models: ...
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1 vote
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### Better default prior for non-negative canonical polyadic decomposition of counts than Exp(1)?

Suppose I have a instance of a random $k$-mode tensor $X_{n_1 \times \ldots \times n_k}$ of count data. I would like to perform non-negative canonical polyadic decomposition of this tensor using ...
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1 vote
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### What "Convolution filters along the time axis" means?

Suppose that I have a tensor of height:25 and width:50. Height is my temporal axis, therefore I have a window of 25 time steps. Therefore my input tensor is: I want to extract temporal features / ...
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### bos_token for a custom Transformer

I am trying to use a Transformer to solve a time-series problem. I built the model using the Pytorch library. And I am planning to train the model from scratch. The model is looking back last L time-...
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### Einstein notation $-$ or another $-$ to denote constraints in high dimensional ILP problems

When discussing marginal sums of arrays in 3 dimensions or more, is it customary in the statistical and/or data science communities to use the Einstein summation convention? Is some other form ...
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### Regarding the quantics tensor train (QTT) format

I originally posted this question in Data Science Stack Exchange, however, I think this forum may be better for this question. I believe I have a fair understanding of the tensor train (TT) format, ...
528 views

### Random forest for tensors

Say we have have input tensor $X \in \mathbb{R}^{T \times N \times P}$ and output tensor $Y \in \mathbb{R}^{T \times N \times K}$, and we aim to build a Random Forests model $Y = f(X)+ \epsilon$. ...
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### Can a Fully Connected layer transform a 4D tensor to a 3D tensor by itself?

Recently, I was researching some topics in biometrics and I stumbled upon this paper. They have a table there (Table 1) in which they state that they used a modified CNN from this paper (Table 9). In ...
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### Machine learning methods for multi-dimensional input and output

I have a large dataset where my input is an $M$-dimensional tensor, and each input has a corresponding $N$-dimensional output. My goal is to train a method to learn outputs from the millions of inputs ...
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### Is there any sort of quadratic SVD for dimensionality reduction?

X-Posted on math.stackexchange, apologies, though I thought this was equally relevant to both communities. I'm wondering if there exists any higher-order SVD for dimensionality reduction. Note that ...
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### Parameters in a neural tensor network

I am reading the paper of "Reasoning With Neural Tensor Networks for Knowledge Base Completion". I read it many times but I couldn't understand the parameters that are used especially the parameter U. ...
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### Best way to represent 3D data for Neural Networks

I want to train a generative model over a dataset where each example is a $X = (N,3)$ matrix representing $N$ points in $\mathbb{R}^3$. The local structure (i.e. the correlations between neighboring ...
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