Questions tagged [information-theory]

Information theory is a branch of applied mathematics, electrical engineering, and computer science involving the quantification of information.

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Does the Lempel-Ziv-Welch algorithm have theoretical or practical use as a language model?

If we encode a string using the LZW algorithm, we obtain a dictionary which maps strings of increasing length onto output symbols and a sequence of output symbols. Is the LZW algorithm useful (...
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Shannon Information Content related to Uncertainty?

I'm a data scientist student currently writing my master thesis which resolves around the Cross Entropy (CE) Loss Function for neural networks. From my understanding, the CE is based on the Entropy, ...
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How to calculate the information conveyed in a message for a given dataset

Given the data sets. Test Set ...
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What does "S" in Shannon's entropy stands for?

I see many machine learning texts using the following notation to represent Shannon's entropy in classification/supervised learning contexts: $$ H(S) = \sum_{i \in Y}p_i \log(p_i) $$ Where $p_i$ is ...
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Self-Attention Summation and Loss of Information

In self-attention, the attention for a word is calculated as: $$ A(q, K, V) = \sum_{i} \frac{exp(q.k^{<i>})}{\sum_{j} exp(q.k^{<j>})}v^{<i>} $$ My question is why we sum over the ...
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A measure of redundancy in mutual information

Mutual information quantifies to what degree $X$ decreases the uncertainty about $Y$. However, to my understanding, it does not quantify "in how many ways" $X$ decreases the uncertainty. E.g....
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Combining "expert-assigned labels" and "real-observed labels"?

Combining "expert-assigned labels" and "real-observed labels"? That is, if I have a data set, where it's possible to have labels that are "true observations" and also ...
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Information bottleneck and deep neural network

I learned about "the information bottleneck view of deep learning." But in a nutshell, what does this tell us? I don't see what the role is of depth in this approach as long as it is larger ...
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Calculating the entropy of a neural network

I am looking to calculate the information contained in a neural network. I am also looking to calculate the maximum information contained by any neural network in a certain amount of bits. These two ...
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Given a sequence of inputs/outputs and a set of nodes that modify that input, can you find the topology of a graph?

I am working on a problem where I have to model a graph topology, where the nodes are logic/arithmetic operations that can be applied to the input. The network receives a multi-dimensional input, and ...
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How to measure the information of covariates in a ML task?

Background Recently, I do 2 different ML projects. One is lending club loan prediction, another is a pravite dataset in online experiment field to predict whether a customer will take the treatment....
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Does Decision tree classifier calculate entropies before transforming categorical features using OneHotEncoder or transformation should be done

I am new to machine learning, and I've got to the point to drop out from it as online tutorials are pretty confusing as well. Entropy and Decision trees One of confusing tutorials was as the ...
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What (probabilistic models) can only output decisions when they are certain?

I'm basically looking for approaches, models, algorithms for the following situation (a fault diagnosis problem): I have an input set $\{x_i\}_{i \in \{1..m\}}$ with $n$ binary features of cases (...
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Conditional Entropy and Mutual Information - Clustering evaluation

First of all, I am doing clustering and I have the true labels for my data. For evaluation, I am using the weighted average of the entropy values for each predicted cluster. I also came across with ...
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Choosing the first node in a decision tree, basic example

I'm wondering whether I'm understanding the process of choosing a node correctly and would like to see if this example makes sense. using the following data : ...
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Feature selection with information gain (KL divergence) and mutual information yields different results

I'm comparing different techniques for feature selection / feature ranking. Two of the techniques under scrutiny are the mutual information (MI) and the information gain (IG) as used in decision trees,...
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Entropy loss from collapsing/merging two categories

Suppose I am counting occurrences in a sequence. For a classical example, let's say I'm counting how many of each kind of car comes down a highway. After keeping tally for a while, I see there are ...
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How to measure word similarity using wordnet for the information theoretic definition as detailed in Resnik 1995? [closed]

Resnik 1995 equation 3 uses count(n) to define P(c). What is count(n)? Any solved example would be appreciated.
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Visualizing mutual information of each convolution layer for image classification problem

I recently came across this paper where the author has proposed a compression based theory on understanding the layers of a DNN. In order to visualize what was going on the authors showed Figure 2 of ...
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Sparse IR with user feedback

I'm considering a problem framing within an information retrieval context. I have a sequence of documents that feature different attributes. In the web context, these would be webpages. One ...
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Is it valid to include your validation data in your vocabulary for NLP?

At the moment, I am following best practices and creating a "bag of words" vector with a vocabulary from the training data. My cross validation (and test) datasets are transformed using this model, ...
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Are deep learning models way over the required capacity for their datasets' estimated entropies?

this question might seem a bit odd. I was doing some self-studies into information theory and decided to do some more formal investigations into deep learning. Please bear with me as I try to explain. ...
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How do you calculate the information capacity of a neural network?

Let's say I wanted to train a neural network to teach it the rules in a decision tree, so I generated a dataset by feeding arrays of random numbers into the pre-trained decision tree, and then used ...
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In CS231n lecture, can't the linear classifier be softmax itself?

I am little bit confused on why the scoring function that is the $f(X,W)$ is chosen to be $W,X$ while they talk about Softmax and SVM loss in this. Can't they take Softmax classifier or SVM ...
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After a Feature Scaling do i have the same initial information?

I'm studying the gradient descent algorithm for single hidden layer neural networks. Suppose that I have an initial dataset and then I use mean normalization in order to scale the features. Why ...
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Measure information gain / loss after a data Transformation operation [closed]

Suppose that we have a dataset of 2 samples : [{1,2,0}, {2,0,0}, {3,1,1}, {4,0,1}, {5,1,1}] (the last element of each row is the class variable) If we want to ...
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Information measure of rank changes?

I'm trying to compute the information content of a function that reranks a list. Perhaps more precisely, I'm trying to compare the information content of different arguments to that function. ...
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What does NIST information weights refer to?

NIST is a metric used to measure the goodness of translation. In the paper, Doddington (2002) introduce the notion of "Information weights" Information weights were computed using N-gram counts ...
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Sigmoid's stability

Analytically, the logarithm of the sigmoid is always defined and finite, because the sigmoid returns values restricted to the open interval (0, 1), rather than using the entire closed interval of ...
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Softmax cost function

In this post, https://cs231n.github.io/linear-classify/#webdemo it mentions "Softmax classifier interprets the scores inside the output vector f as the unnormalized log probabilities." Aren't we ...
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A practical reason to use Cross-entropy as a error-function in Neural networks?

Cross-entropy tends to allow errors to change weights even when nodes saturate (which means that their derivatives are asymptotically close to 0.) Link Why is the above statement true? Figures ...
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The meaning of the difference of two entropy values

I want to understanding the meaning of the difference of two information entropy values. I have the following scenario. Let $x$ be a number of hours a user spend on some video sharing websites. Thus, ...
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Why the number of neurons or convolutions chosen equal powers of two?

In the overwhelming number of works devoted to the neural networks, the authors suggest arhitechure in which each layer is a numbers of neurons is power of 2 what are the theoretical reasons(...
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Why we use information gain over accuracy as splitting criterion in decision tree?

In decision tree classifier most of the algorithms use Information gain as spiting criterion. We select the feature with maximum information gain to split on. I think that using accuracy instead of ...
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5 votes
1 answer
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How to estimate the mutual information numerically?

Suppose I have a sample {$z_i$}$_{i\in[0,N]}$ = {($x_i,y_i$)}$_{i\in[0,N]}$ which commes from a probability distribution $p_z(z)$. How can I use it to estimate the mutual information between X and Y ? ...
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When should I use Gini Impurity as opposed to Information Gain (Entropy)?

Can someone practically explain the rationale behind Gini impurity vs Information gain (based on Entropy)? Which metric is better to use in different scenarios while using decision trees?
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