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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Understandable way of thinking about higher order tensors
I study deep learning and the one of the major problem I face is I can't imagine shape of higher order tensors in my head.
for instance -
A 2d tensor - (x,y) is a rectangle with x,y along its length ...
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Compact/Vectorized Multiclass Logistic Regression Hessian
I know that the Hessian of the categorical cross entropy w.r.t the weights is given by
$$\frac{\partial^2 L}{\partial w^2} = \sum_{i=1}^{m} (Diag(\hat{y}_i)-\hat{y}_i^T \hat{y}_i) \otimes x_i^T x_i$$
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Why modeling known entries improves Tensor completion problem?
In the following paper:
"Scalable tensor factorizations with missing data" by Evrim Acar
Authors mention on page 2 that unlike conventional "CP" method which models both known and unknown values, they ...
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Mismatch in input shape - Inference server exception
I am using Nvidia's tensorrt-inference server. We have a model trained and deployed in the inference server. The input image shape is (224,224,3) and output shape is 224,224,1.
Currently I pass a ...
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Why are some robust algorithms valid for Tucker decomposition, but not for CP decomposition?
I have been reading up about CP and Tucker decomposition.
It makes sense that CP decomposition is a special case of Tucker decomposition, where the core tensor is super-diagonal. However, if this is ...
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Diffusion tensor as a covariance matrix
TLDR: In nuclear magnetic resonance (NMR), to study molecular diffusion we assume that molecules displace in 3D space according to a trivariate gaussian distribution. The variables are then the ...
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Higher moments of linear regression residuals?
I previously asked this on Math StackExchange, with no success, but this post will add to that with some simulations.
Background
In the following linear regression with i.i.d $\epsilon_i$ $(i = 1, \...
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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, ...
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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 higher-order SVD (quadratic and above) 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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57 views
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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1answer
153 views
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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1answer
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Satellite data pre-processing for Keras CNNs [closed]
I’m looking at satellite data and want to do object detection using CNNs in Keras. I’m currently pre-processing the data (turning them into tensors) that I’ve obtained which include the original ...
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Shape of a tensor [closed]
Suppose I have a variable that looks like this
[[[1., 2., 3.]], [[7., 8., 9.]]]
I have read this is a rank 3 tensor with shape ...
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References on tensor algebra for machine learning? [duplicate]
So tensors come up a lot in machine learning in various settings. Any math major will have studied linear algebra heavily and it's usually much simpler to use linear operators and the corresponding ...
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Tensor Classification Models
Aside from Convolution Neural Networks, are there any other methods that allow for classification of Tensors? My observations consist of multi-dimensional tensors with height of 1, where each channel ...
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CP decomposition for tensor factorization
I am trying to understand CP decomposition for a three way tensor. Lets have a tensor which has the dimensions I by J by K. When we apply CP decomposition, it decomposes the tensor as a sum of a rank-...
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289 views
Fitting Tensor Product P-splines, Penalty Parameters
I am working with the mgcv package in r and I am fitting tensor product P-splines.
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Implementation of algorithm to determine next basket recommendation?
I hope I am asking in right forum, and forgive me, if I am wrong.
I am trying to implement an algorithm based on an open paper ...
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Validating decomposition of Synthetic Tensor generated from Unevenly Sampled Tensor
I have a 3-way tensor generated from 7 experiments, with each experiment being matricized and becoming a frontal slice of the tensor (thus mode-3 is of length 7). The data is generated from ...
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Difference between samples, time steps and features in neural network
I am going through the following blog on LSTM neural network:
http://machinelearningmastery.com/understanding-stateful-lstm-recurrent-neural-networks-python-keras/
The author reshapes the input ...
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1answer
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Tensor method under high noise
Tensor methods give good results under low approximation error. (e.g. at 7min http://videolectures.net/iclr2016_anandkumar_nonconvex_learning/). I am wondering how do they do when the noise in the ...
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1answer
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Usage of tensor notation in statistics
A friend of mine (mathematician) basically told me I shouldn't bother with matrix algebra and should focus on tensor analysis/manipulation. He said it's much more general and intuitive. I've been ...
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Tensors in neural network literature: what's the simplest definition out there?
In the neural network literature, often we encounter the word "tensor".
Is it different from a vector? And from a matrix? Have you got any specific example that clarifies its definition?
I'm a bit ...
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Logistic Tensor Regression
Say there are users and they view articles and click (or not click) on articles. I represent the $i$-th user as $x_i$, a $D \times1 $ vector and $j$-th article as $z_j$, a $C \times 1$vector. The ...
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Intuition behind using tensors ? [closed]
I am trying to build a recommendation model by using a tensor. In order to recommend an article to a user, I have built a model to predict users' preferable articles.
I am labeling articles based on ...
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9answers
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Why the sudden fascination with tensors?
I've noticed lately that a lot of people are developing tensor equivalents of many methods (tensor factorization, tensor kernels, tensors for topic modeling, etc) I'm wondering, why is the world ...
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The meaning of tensors in the neural network community [duplicate]
In the neural network community, is a tensor pretty much always just a multi-dimensional array?
