entropy | The main firmware
kandi X-RAY | entropy Summary
kandi X-RAY | entropy Summary
The main firmware is in the me sub-directory. The rest is auxiliary components (such as bootloader) and tools.
Support
Quality
Security
License
Reuse
Top functions reviewed by kandi - BETA
Currently covering the most popular Java, JavaScript and Python libraries. See a Sample of entropy
entropy Key Features
entropy Examples and Code Snippets
Community Discussions
Trending Discussions on entropy
QUESTION
Is the Shannon-Fano coding as described in Fano's paper The Transmission of Information (1952) really ambiguous?
In Detail:3 papers
Claude E. Shannon published his famous paper A Mathematical Theory of Communication in July 1948. In this paper he invented the term bit as we know it today and he also defined what we call Shannon entropy today. And he also proposed an entropy based data compression algorithm in this paper. But Shannon's algorithm was so weak, that under certain circumstances the "compressed" messages could be even longer than in fix length coding. A few month later (March 1949) Robert M. Fano published an improved version of Shannons algorithm in the paper The Transmission of Information. 3 years after Fano (in September 1952) his student David A. Huffman published an even better version in his paper A Method for the Construction of Minimum-Redundancy Codes. Hoffman Coding is more efficient than its two predecessors and it is still used today. But my question is about the algorithm published by Fano which usually is called Shannon-Fano-Coding.
The algorithm
This description is based on the description from Wikipedia. Sorry, I did not fully read Fano's paper. I only browsed through it. It is 37 pages long and I really tried hard to find a passage where he talks about the topic of my question, but I could not find it. So, here is how Shannon-Fano encoding works:
- Count how often each character appears in the message.
- Sort all characters by frequency, characters with highest frequency on top of the list
- Divide the list into two parts, such that the sums of frequencies in both parts are as equal as possible. Add the bit
0
to one part and the bit1
to the other part. - Repeat step 3 on each part that contains 2 or more characters until all parts consist of only 1 character.
- Concatenate all bits from all rounds. This is the Shannon-Fano-code of that character.
An example
Let's execute this on a really tiny example (I think it's the smallest message where the problem appears). Here is the message to encode:
ANSWER
Answered 2022-Mar-08 at 19:00To directly answer your question, without further elaboration about how to break ties, two different implementations of Shannon-Fano could produce different codes of different lengths for the same inputs.
As @MattTimmermans noted in the comments, Shannon-Fano does not always produce optimal prefix-free codings the way that, say, Huffman coding does. It might therefore be helpful to think of it less as an algorithm and more of a heuristic - something that likely will produce a good code but isn't guaranteed to give an optimal solution. Many heuristics suffer from similar issues, where minor tweaks in the input or how ties are broken could result in different results. A good example of this is the greedy coloring algorithm for finding vertex colorings of graphs. The linked Wikipedia article includes an example in which changing the order in which nodes are visited by the same basic algorithm yields wildly different results.
Even algorithms that produce optimal results, however, can sometimes produce different optimal results based on tiebreaks. Take Huffman coding, for example, which works by repeatedly finding the two lowest-weight trees assembled so far and merging them together. In the event that there are three or more trees at some intermediary step that are all tied for the same weight, different implementations of Huffman coding could produce different prefix-free codes based on which two they join together. The resulting trees would all be equally "good," though, in that they'd all produce outputs of the same length. (That's largely because, unlike Shannon-Fano, Huffman coding is guaranteed to produce an optimal encoding.)
That being said, it's easy to adjust Shannon-Fano so that it always produces a consistent result. For example, you could say "in the event of a tie, choose the partition that puts fewer items into the top group," at which point you would always consistently produce the same coding. It wouldn't necessarily be an optimal encoding, but, then again, since Shannon-Fano was never guaranteed to do so, this is probably not a major concern.
If, on the other hand, you're interested in the question of "when Shannon-Fano has to break a tie, how do I decide how to break the tie to produce the optimal solution?," then I'm not sure of a way to do this other than recursively trying both options and seeing which one is better, which in the worst case leads to exponentially-slow runtimes. But perhaps someone else here can find a way to do that>
QUESTION
My code :
...ANSWER
Answered 2022-Feb-23 at 07:08Try something like this:
QUESTION
I am currently attempting to estimate the parameters of a logistic regression model "by hand" on the iris
dataset via minimisation of cross-entropy. Please note, when I say iris
dataset, it has been changed such that there are only two classes - Setosa and Other. It was also normalised via the scale
function:
ANSWER
Answered 2022-Feb-20 at 10:38The main issue is that you have "complete separation" in your dataset. With those predictors, you can identify Species_n
without any error at all. In this kind of situation, the logistic model has no MLE, it improves more and more as the estimated coefficients get more extreme in the right direction.
The way to detect this is to look at the predicted probabilities or logits. When I ran your model once, I got estimates that were
QUESTION
I have 4 functions for some statistical calculations in complex networks analysis.
...ANSWER
Answered 2022-Jan-26 at 15:38It looks like, in calculate_community_modularity
, you use greedy_modularity_communities
to create a dict, modularity_dict
, which maps a node in your graph to a community
. If I understand correctly, you can take each subgraph community in modularity_dict
and pass it into shannon_entropy
to calculate the entropy for that community.
this is pseudo code, so there may be some errors. This should convey the principle, though.
after running calculate_community_modularity
, you have a
dict like this, where the key is each node, and the value is that which the community belongs to
QUESTION
Can someone explain why adding random numbers to the loss does not affect the predictions of this Keras model? Every time I run it I get a very similar AUC for both models but I would expect the AUC from the second model to be close to 0.5. I use Colab.
Any suggestions why this might be happening?
...ANSWER
Answered 2022-Jan-24 at 14:12The training is guided by the gradient of the loss with respect to the input.
The random value that you add to the loss in the second model is independent form the input, so it will not contribute to the gradient of the loss during training. When you are running the prediction you are taking the the model output (before the loss function), so that's not affected as well.
QUESTION
I'm working on a statistics project involving cards and shuffling, and I've run across an issue with random number generation.
From a simple bit of math there are 52! possible deck permutations, which is approximately 2^226. I believe this means that I need a random number generator with a minimum of 226 bits of entropy, and possibly more (I'm not certain of this concept so any help would be great).
From a quick google search, the Math.random()
generator in Java has a maximum of 48 bits of entropy, meaning that the vast majority of possible deck combinations would not be represented. So this does not seem to be the way to go in Java.
I was linked to this generator but it doesn't have a java implementation yet. Also for a bit of context here is one of my shuffling algorithms (it uses the Fisher-Yates method). If you have any suggestions for better code efficiency that would be fantastic as well.
...ANSWER
Answered 2022-Jan-15 at 01:10Have you looked into the recent additions that are included in JDK 17?
There are plenty of algorithms available:
For shuffling cards you likely don't need something that is cryptographically secure.
Using Collections.shuffle should do the trick if you provide a decent RNG.
QUESTION
When the first item was hovered and the others would activate too. But when the second item was hovered and the others won't work. How can I let every item animation trigger one by one?
...ANSWER
Answered 2022-Jan-11 at 09:30In this example there is an SVG element for each image. This includes a with a unique id and a
where the clip-path is defined. The
also have a unique id. The result is that a unique image is making use of a unique clip-path, and the animation is started and ended with reference to that particular image.
If there are many images that need this clip-path we can agree that this is not an optimal solution. Reusing an already defined clip-path would be better, but as you discovered a "common" clip-path for all images will animate the clip-path on all the images at the same time. I have researched this and also tried a bit of JavaScript and reading the spec for begin-value without any clues on solving this.
Going for a CSS based animation could be a solution, but at the same time it it also limited what you can do in a setup like that.
QUESTION
I am training a neural network to distinguish between three classes. Naturally, I went for PyTorch's CrossEntropyLoss
. During experimentation, I realized that the loss was significantly higher when a Softmax
layer was put at the end of the model. So I decided to experiment further:
ANSWER
Answered 2021-Dec-30 at 14:51From the docs, the input to CrossEntropyLoss
"is expected to contain raw, unnormalized scores for each class". Those are typically called logits.
There are two questions:
- Scaling the logits should not yield the same cross-entropy. You might be thinking of a linear normalization, but the (implicit) softmax in the cross-entropy normalizes the exponential of the logits.
- This causes the learning to optimize toward larger values of the logits. This is exactly what you want because it means that the network is more "confident" of the classification prediction. (The posterior p(c|x) is closer to the ground truth.)
QUESTION
I am running Fuzzy C-Means Clustering using e1071
package. I want to decide the optimum number of clusters based on fuzzy performance index (FPI) (extent of fuzziness) and normalized classification entropy (NCE) (degree of disorganization of specific class) given in the following formula
where c is the number of clusters and n is the number of observations, μik is the fuzzy membership and loga is the natural logarithm.
I am using the following code
...ANSWER
Answered 2021-Nov-15 at 07:34With available equations, we can program our own functions. Here, the two functions use equations present in the paper you suggested and one of the references the authors cite.
QUESTION
I'm trying to show a tree visualisation using plot_tree, but it shows a chunk of text instead:
...ANSWER
Answered 2021-Oct-27 at 07:27In my case, it works with a simple "show":
Community Discussions, Code Snippets contain sources that include Stack Exchange Network
Vulnerabilities
No vulnerabilities reported
Install entropy
Support
Reuse Trending Solutions
Find, review, and download reusable Libraries, Code Snippets, Cloud APIs from over 650 million Knowledge Items
Find more librariesStay Updated
Subscribe to our newsletter for trending solutions and developer bootcamps
Share this Page