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How can I display all CPT of a DBN in the Bayes Net Toolbox (MATLAB - BNT)?
In the Bayes Net Toolbox, what is called Dynamic Bayesian Network is in fact just a Temporal Bayesian Network in which we can specify a different structure for the first time-slice: http://bnt.googlecode.com/svn/trunk/docs/usage_dbn.html : Note that "temporal Bayesian network" would be a better name than "dynamic Bayesian network", since it is assumed that the model structure does not change, but the term DBN has become entrenched. We also normally assume that the parameters do not change, i.e., the model is time-invariant. However, we can always add extra hidden nodes to represent the current "regime", thereby creating mixtures of models to capture periodic non-stationarities. [...] To specify a DBN, we need to define the intra-slice topology (within a slice),

Categories : Matlab

Bayes Network for classification in Matlab (BNT)
The conditional probability table (CPT) for 'class' should have 8 (2*2*2) elements in this case. The posterior output (marg.T) of the inference engine seems right for a binary variable. It reads as: "with 0.8 probability the 'class' node is in state 1, and with 0.2 probability it is in state 2". From this point on, it is up to the user to decide whether to appoint 'class' to state 1 or 2. When it comes to classification, in the simplest (and not very advisable) case, you can define a posterior probability threshold of 0.5 and say: if P(class=1)> 0.5 class = 1 else class = 2 end In assessing the performance of your binary classification, you can look into predictive accuracy or Area Under the ROC curve (AUC) or do more intelligent things that take into account the prior probabilitie

Categories : Matlab

gaussian mixture model probability matlab
In one dimension, the maximum value of the pdf of the Gaussian distribution is 1/sqrt(2*PI). So in 50 dimensions, the maximum value is going to be 1/(sqrt(2*PI)^50) which is around 1E-20. So the values of the pdf are all going to be of that order of magnitude, or smaller.

Categories : Matlab

How to get the standard deviation from gaussian fitted curve in Matlab
The output of fy says that you are fitting a model that consist of a linear combination of two Gaussian functions. The functional form of the model is: fy(x) = a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-b2)/c2)^2) Remembering that a Gaussian is defined as: f(x) = exp(-(x-x0)^2/(2*s^2)) where: x0 is the mean, s is the std.dev. then the standard deviation of each Gaussian in your model can be computed as (respectively): s1 = c1/sqrt(2) s2 = c2/sqrt(2) See http://en.wikipedia.org/wiki/Gaussian_function for more infomation.

Categories : Matlab

Randomly generating numbers within a fixed non-Gaussian distribution in matlab
Not quite sure what you are asking precisely, but I guess you could take a look at the random() function in the statistics toolbox: >> help random RANDOM Generate random arrays from a specified distribution. R = RANDOM(NAME,A) returns an array of random numbers chosen from the one-parameter probability distribution specified by NAME with parameter values A. R = RANDOM(NAME,A,B) or R = RANDOM(NAME,A,B,C) returns an array of random numbers chosen from a two- or three-parameter probability distribution with parameter values A, B (and C). The size of R is the common size of the input arguments. A scalar input functions as a constant matrix of the same size as the other inputs. R = RANDOM(NAME,A,M,N,...) or R = RANDOM(NAME,A,[M,N,...]) returns an M-by-N-by-...

Categories : Matlab

Naive Bayes probability always 1
"...the probability outputs from predict_proba are not to be taken too seriously" I'm the guy who wrote that. The point is that naive Bayes tends to predict probabilities that are almost always either very close to zero or very close to one; exactly the behavior you observe. Logistic regression (sklearn.linear_model.LogisticRegression or sklearn.linear_model.SGDClassifier(loss="log")) produces more realistic probabilities. The resulting GaussianNB object is very big (~300MB), and prediction is rather slow: around 1 second for one text. That's because GaussianNB is a non-linear model and does not support sparse matrices (which you found out already, since you're using toarray). Use MultinomialNB, BernoulliNB or logistic regression, which are much faster at predict time and also s

Categories : Python

Bayes network classification
Assuming all variables you mention are categorical and the edge directions are from up to down: Priors: In the first Naive Bayes example, the conditional probability table (CPT) of 'class' consists solely of its prior distribution because it is a root node, i.e. does not have any parents. If 'class' can take on 2 states (e.g. black and white), its CPT will consist of 2 values. In the second Bayesian Network (BN) example, the CPT of 'class' is dependent on 'cause1' and 'consequence'. Lets say 'consequence' has 3 states, 'cause1' has 4 states and as before 'class' has 2 states. In this case, the CPT of 'class' would contain 3*4*2 values. When you are learning this CPT, you can incorporate your prior beliefs as a dirichlet distribution (if all variables are categorical). For an example of

Categories : Machine Learning

Bayes Learning - MAP hypotesis
Such question should be asked (and now probably migrated) on the math.stackexchange.com or stats.stackexchange.com . Your question is basic application of the Bayes Theorem P(Y=0|h1)P(h1) 0.2*0.2 0.04 P(h1|Y=0) = ------------- = ------- = ------ P(Y=0) P(Y=0) P(Y=0) P(Y=0|h2)P(h2) 0.3*0.4 0.12 P(h2|Y=0) = -------------- = ------- = ------ P(Y=0) P(Y=0) P(Y=0) So the h2 is the more probable hypothesis, as P(Y=0)>0

Categories : Machine Learning

Model in Naive Bayes
Naive Bayes constructs estimations of conditional probabilities P(f_1,...,f_n|C_j), where f_i are features and C_j are classes, which, using bayes rule and estimation of priors (P(C_j)) and evidence (P(f_i)) can be translated into x=P(C_j|f_1,...,f_n), which can be roughly read as "Given features f_i I think, that their describe object of class C_j and my certainty is x". In fact, NB assumes that festures are independent, and so it actualy uses simple propabilities in form of x=P(f_i|C_j), so "given f_i I think that it is C_j with probability x". So the form of the model is set of probabilities: Conditional probabilities P(f_i|C_j) for each feature f_i and each class C_j priors P(C_j) for each class KNN on the other hand is something completely different. It actually is not a "learne

Categories : Machine Learning

naive bayes classifier error in r
Seems like building of the model failing (and as a result the classifier is not constructed). Without looking at your data, my best guess would be that you have incomplete cases. You could try removing cases with missing data using complete.cases as follows. d <- read.table("Modeling_Data.txt",header=FALSE,sep=" ",comment.char="",quote="") # remove incomplete cases d[complete.cases(d),] # divide into training and test data 70:30 trainingIndex <- createDataPartition(d$V32, p=.7, list=F)

Categories : R

Calculation of probabilities in Naive Bayes in C#
This code is called over and over again for each particular word w in the text (e.g. tweet) being analyzed. All the variables are conditional probabilities estimated using frequencies. bw is the probability that the word w is seen given that the word is a category 1 text gw is the probability that the word w is seen given that the word is a category 2 text pw rescales the probability bw so that rarely seen words are on a similar scale to frequently seen words (mathematically, the division indicates that pw is a conditional probability) fw simply shifts the scale so that pw can't be zero (or one). So if, for example, pw=0 and n=10, fw = ((1 * 0.5) + (10 * 0)) / (1 + 10) = 0.045. (In general, a good way to understand this code is to play around with some different numbers and see what ha

Categories : C#

Understanding this application of a Naive Bayes Classifier
First of all, the formula P(Terrorism | W) = P(Terrorism) x P(kill | Terrorism) x P(bomb | Terrorism) x P(kidnap | Terrorism) x P(music | Terrorism) x P(movie | Terrorism) x P(TV | Terrorism) isn't quite right. You need to divide that by P(W). But you hint that this is taken care of later when it says that "they do a few sums", so we can move on to your main question. Traditionally when doing Naive Bayes on text classification, you only look at the existence of words, not their counts. Of course you need the counts to estimate P(word | class) at train time, but at test time P("music" | Terrorism) typically means the probability that the word "music" is present at least once in a Terrorism document. It looks like what the implementation you are dealing with is doing is it's trying to

Categories : Misc

Normal Bayes Classifer Negative Samples
First of all, you need to decide whether you are going to do recognition. Recognition and detection are different processes. are you going to have 3 systems detecting cars, trucks and animals respectively or are you going to have 1 system detecting all of these, but also classifying somehow with a recognition step. Second, "animal" detection is a hard process, where "cat" detection is easier. Please narrow down your range and make the positives similar. Check this link for a similar problem. Third, as you already noticed, you actually need more negatives than positives for a proper training.

Categories : Opencv

Naive Bayes Classification for Categorical Data
because labels of your dataset are in numeric format, R decide to use regression instead of classification. change labels of data set to characters instead of numbers. so R will not confuse.

Categories : R

Document Classification using Naive Bayes classifier
A lot of this gets into how good "accuracy" is as a measure of performance, and that depends on your problem. If misclassifying "A" as "B" is just as bad/ok as misclassifying "B" as "A", then there is little reason to do anything other than just mark everything as "A", since you know it will reliably get you a 98% accuracy (so long as that unbalanced distribution is representative of the true distribution). Without knowing your problem (and if accuracy is the measure you should use), the best answer I could give is "it depends on the data set". It is possible that you could get past 99% accuracy with standard naive bays, though it may be unlikely. For Naive Bayes in particular, one thing you could do is to disable the use of priors (the prior is essentially the proportion of each class).

Categories : Machine Learning

How to improve the accuracy of a Naive Bayes Classifier?
This appears to be the classic problem of "overfitting"... where you get a very high % accuracy on the training set, but a low % in real situations. You probably need more training instances. Also, there is the possibility that the 26 categories don't correlate to the features you have. Machine Learning isn't magical and needs some sort of statistical relationship between the variables and the outcomes. Effectively, what NBC might be doing here is effectively "memorizing" the training set, which is completely useless for questions outside of memory.

Categories : Performance

how to Load CSV Data in scikit and using it for Naive Bayes Classification
The following should get you started you will need pandas and numpy. You can load your .csv into a data frame and use that to input into the model. You all so need to define targets (0 for negatives and 1 for positives, assuming binary classification) depending on what you are trying to separate. from sklearn.naive_bayes import GaussianNB import pandas as pd import numpy as np # create data frame containing your data, each column can be accessed # by df['column name'] df = pd.read_csv('/your/path/yourFile.csv') target_names = np.array(['Positives','Negatives']) # add columns to your data frame df['is_train'] = np.random.uniform(0, 1, len(df)) <= 0.75 df['Type'] = pd.Factor(targets, target_names) df['Targets'] = targets # define training and test sets train = df[df['is_train']

Categories : Python

ChoiceModelR - Hierarchical Bayes Multinomial Logit Model
I know that this may not be helpful since you posted so long ago, but if it comes up again in the future, this could prove useful. One of the most common reasons for this error (in my experience) has been that either the scenario variable or the alternative variable is not in ascending order within your data. id scenario alt x1 ... y 1 1 1 4 1 1 1 2 1 0 1 3 1 4 2 1 3 2 5 0 2 1 4 3 1 2 1 5 1 0 2 2 1 4 2 2 2 2 3 0 This dataset will give you errors since the scenario and alternative variables must be ascending, and they must not skip any values.

Categories : R

naive bayes, 15 features on 35instances dataset - 7 classes
naive Bayes works well when your features don't effect each other... but it works very well when you have small data-set on the other hand you can try logistic regression or SVM but in real World scenarios your algorithm doesn't matter that much , your Dataset(instances,features) is more important

Categories : Java

Classifying Multinomial Naive Bayes Classifier with Python Example
The original code trains on the first 100 examples of positive and negative and then classifies the remainder. You have removed the boundary and used each example in both the training and classification phase, in other words, you have duplicated features. To fix this, split the data set into two sets, train and test. The confusion matrix is higher (or different) because you are training on different data. The confusion matrix is a measure of accuracy and shows the number of false positives etc. Read more here: http://en.wikipedia.org/wiki/Confusion_matrix

Categories : Python

Naive Bayes Classifier in e1071 package [R] - Editing Data
Just figured it out Essentially, the classifier is a set of 4 values, the apriori probabilities, the mean and standard deviations of each of the probabilities, the different classes, and the original call. Each of those values is a nested list with one item, and if you keep on delving into the individual lists you can get at the individual items, including the individual probability matrices, and work from there. The first value of each is the mean, and the second is the standard deviation. From there you can pull whatever data you want, and edit to your heart's extent.

Categories : R

Sklearn naive bayes classifier for data belonging to the same class
The naive Bayes classifier classifies each input individually (not as a group). If you know that all of the inputs belong to the same (but unknown) class, then you need to do some additional work to get your result. One option is to select the class with the greatest count in the result from clf.predict but that might not work well if you are only have two instances in the group. Another option would be to call predict_proba for the GaussianNB classifier, which will return the probabilities of all classes for each of the inputs. You can then use the individual probabilities (e.g., you could just sum them for each class) to decide how you want to classify the group. You could even combine the two approaches - Use predict and select the class with the highest count but use predict_proba to

Categories : Python

R: Naives Bayes classifier bases decision only on a-priori probabilities
It looks like you trained the model using whole sentences as inputs, while it seems that you want to use words as your input features. Usage: ## S3 method for class 'formula' naiveBayes(formula, data, laplace = 0, ..., subset, na.action = na.pass) ## Default S3 method: naiveBayes(x, y, laplace = 0, ...) ## S3 method for class 'naiveBayes' predict(object, newdata, type = c("class", "raw"), threshold = 0.001, ...) Arguments: x: A numeric matrix, or a data frame of categorical and/or numeric variables. y: Class vector. In particular, if you train naiveBayes this way: x <- c("john likes cake", "marry likes cats and john") y <- as.factor(c("good", "bad")) bayes<-naiveBayes( x,y ) you get a classifier able to recognize just these two sentences: Naive Ba

Categories : R

scikit learn use multinomial naive bayes for a trigram classifier?
CountVectorizer will extract trigrams for you (using ngram_range=(3, 3)). The text feature extraction documentation introduces this. Then, just use MultinomialNB exactly like before with the transformed feature matrix. Note that this is actually modeling: P(document | label) = P(wordX, wordX-1, wordX-2 | label) * P(wordX-1, wordX-2, wordX-3 | label) * ... How different is that? Well, that first term can be written as P(wordX, wordX-1, wordX-2 | label) = P(wordX | wordX-1, wordX-2, label) * P(wordX-1, wordX-2 | label) Of course, all the other terms can be written that way too, so you end up with (dropping the subscripts and the conditioning on the label for brevity): P(X | X-1, X-2) P(X-1 | X-2, X-3) ... P(3 | 2, 1) P(X-1, X-2) P(X-2, X-3) ... P(2, 1) Now, P(X-1, X-2) can be written

Categories : Python

Predicting Classifications with Naive Bayes and dealing with Features/Words not in the training set
From a practical perspective (keeping in mind this is not all you're asking), I'd suggest the following framework: Train a model using an initial train set, and start using it for classificaion Whenever a new word (with respect to your current model) appears, use some smoothing method to account for it. e.g. Laplace smoothing, as suggested in the question, might be a good start. Periodically retrain your model using new data (usually in addition to the original train set), to account for changes in the problem domain, e.g. new terms. This can be done on preset intervals, e.g once a month; after some number of unknown words was encountered, or in an online manner, i.e. after each input document. This retrain step can be done manually, e.g. collect all documents containing unknown terms

Categories : Machine Learning

Naive Bayes Classifier, Explain model fitting and prediction algorithms
Please see below. If you want more details of the mathematics involved you might be better off posting on cross-validated. Could someone outline why the log-sum-exp trick is/needs to be done? This is for numerical stability. If you search for "logsumexp" you will see several useful explanations. E.g., https://hips.seas.harvard.edu/blog/2013/01/09/computing-log-sum-exp, and log-sum-exp trick why not recursive. Essentially, the procedure avoids numerical error that can occur with numbers that are too big / too small. specifically what the argument Li,: reads as The i means take the ith row, and the : means take all values from that row. So, overall, Li,: means the ith row of L. The colon : is used in Matlab (and its open source derivative Octave) to mean "all indices" when subscr

Categories : Algorithm

How to use WEKA Machine Learning for a Bayes Neural Network and J48 Decision Tree
Here is one way to do it with the command-line. This information is found in Chapter 1 ("A command-line primer") of the Weka manual that comes with the software. java weka.classifiers.trees.J48 -t training_data.arff -T test_data.arff -p 1-N where: -t <training_data.arff> specifies the training data in ARFF format -T <test_data.arff> specifies the test data in ARFF format -p 1-N specifies that you want to output the feature vector and the prediction, where N is the number of features in your feature vector. For example, here I am using soybean.arff for both training and testing. There are 35 features in the feature vector: java weka.classifiers.trees.J48 -t soybean.arff -T soybean.arff -p 1-35 The first few lines of the output look like: === Predictions on test dat

Categories : Machine Learning

Save and Load testing classify Naive Bayes Classifier in NLTK in another method
I don't have the environment setup to test out your code, but I have the feeling it's not right in the part where you save/load the pickle. Referring to the Storing Taggers section of the NLTK book, I would change your code and do it like this: def save_classifier(classifier): f = open('my_classifier.pickle', 'wb') pickle.dump(classifier, f, -1) f.close() def load_classifier(): f = open('my_classifier.pickle', 'rb') classifier = pickle.load(f) f.close() return classifier Hope it helps.

Categories : Python

Blur.js is probably what you are looking for! http://blurjs.com/ It works for moving DIVs as well, which satisfies your presupposition! Have a look at the draggable example $('.target').blurjs({ draggable: true, overlay: 'rgba(255,255,255,0.4)' });

Categories : Javascript

gaussian binning of data
It sounds like you have a single measurement at a single point (X=100, e=5000), and also know the value of the FWHM (FWHM = 4). If this is indeed the case, you can compute the standard deviation sigma like so: sigma = FWHM/ 2/sqrt(2*log(2)); and you can make bins like so: [N, binCtr] = hist(sigma*randn(e,1) + X, Nbins); where N is the amount of electrons in each bin, binCtr are the bin centers, Nbins is the amount of bins you want to use. If the number of electrons gets large, you could run out of memory. In such cases, it's better to do the same thing but in smaller batches, like so: % Example data FWHM = 4; e = 100000; X = 100; Nbins = 100; % your std. dev. sigma = FWHM/ 2/sqrt(2*log(2)); % Find where to start with the bin edges. That is, find the point % where the PDF i

Categories : Matlab

Gaussian fit to plot, plotted using bar(x,y)
A trick, which however does NOT recover the original raw data (therefore the fit suffers also from the approximations introduced by the binning), is to decode with the run-length algorithm your x, and run histfit() on that data: % data from your previous question x = [0 0.0278 0.0556 0.0833 0.1111 0.1389 0.1667 0.1945 0.2222]; y = [1 3 10 13 28 53 66 91 137]; % histfit histfit(rude(y,x),9,'normal') where you can find the run-length encoding/decoding function on FEX: rude(). The result:

Categories : Matlab

Not sure how to fit data with a gaussian python
It seems like you can just use the definitions of the mean and covariance parameters to fit them using maximum likelihood estimates from your data, right ? import numpy as np data = np.loadtxt("/home/***/****/***", usecols=(2, 3)) mu = data.mean(axis=0) sigma = np.cov(data, rowvar=0) In my understanding, this is what "fitting" means. However, it sounds like you're then looking to show these quantities on a plot. This can be a little trickier, but only because you need to use some linear algebra to find the eigenvectors of the estimated covariance matrix, and then use those to draw the covariance ellipse. import matplotlib.pyplot as plt from matplotlib.patches import Ellipse # compute eigenvalues and associated eigenvectors vals, vecs = np.linalg.eigh(sigma) # compute "tilt" of ellip

Categories : Python

How do you implement a calculated Gaussian kernel?
It sounds like you want to compute a convolution of the original image with a Gaussian kernel, something like this: blurred[x][y] = Integral (kernel[s][t] * original[x-s][y-t]) ds dt There are a number of techniques for that: Direct convolution: go through the grid and compute the above integral at each point. This works well for kernels with very small support, on the order of 5 grid points in each direction, but for kernels with larger support becomes too slow. For Gaussian kernels a rule of thumb for truncating support is about 3*sigma, so it's not unreasonable to do direct convolution with sigma under 2 grid points. Fast Fourier Transform (FFT). This works reasonable fast for any kernel. Therefore FFT became the standard way to compute convolution of nearly anything with nearly an

Categories : C++

Gaussian filtering a image with Nan in Python
The simplest thing would be to turn nans into zeros via nan_to_num. Whether this is meaningful or not is a separate question.

Categories : Python

How to obtain a gaussian filter in python
In general terms if you really care about getting the the exact same result as MATLAB, the easiest way to achieve this is often by looking directly at the source of the MATLAB function. In this case, edit fspecial: ... case 'gaussian' % Gaussian filter siz = (p2-1)/2; std = p3; [x,y] = meshgrid(-siz(2):siz(2),-siz(1):siz(1)); arg = -(x.*x + y.*y)/(2*std*std); h = exp(arg); h(h<eps*max(h(:))) = 0; sumh = sum(h(:)); if sumh ~= 0, h = h/sumh; end; ... Pretty simple, eh? It's <10mins work to port this to Python: import numpy as np def matlab_style_gauss2D(shape=(3,3),sigma=0.5): """ 2D gaussian mask - should give the same result as MATLAB's fspecial('gaussian',[shape],[sigma]) """ m,n = [(ss-1.

Categories : Python

Fitting gaussian to data in python
You currrently draw a scatter plot. The docs have a demo for plotting a histogram, which might be Gaussian, depending on the distribution of your data. You need something like plt.hist(x, 50, normed=1, histtype='stepfilled') There are further demos here

Categories : Python

RenderScript Intrinsics Gaussian blur
I'm guessing you've got some issue with the UI parts rather than the RS parts. The RS parts look fine; maybe try a outputBitmap.prepareToDraw() after the RS bits have finished? Note that in general it's not a great idea to create and destroy RS contexts in the critical path like that. There's potentially a nontrivial startup/teardown cost depending on the hardware resources that have to be allocated, so it would be much better to allocate it at startup and use it for the lifetime of the application.

Categories : Android

SVG Gaussian Blur not working in Firefox
it is just that you have a crazy hudge value. try this: <svg xmlns="http://www.w3.org/2000/svg" version="1.1"> <defs> <filter id="f1" x="0" y="0"> <feGaussianBlur stdDeviation="5" /> </filter> </defs> </svg>

Categories : Jquery

1D gaussian filter over non equidistant data
use this: function yy = smooth1D(x,y,delta) n = length(y); yy = zeros(n,1); for i=1:n; ker = sqrt(6.0/pi*delta^2)*exp(-6.0*(x-x(i)).^2 /delta^2); %the gaussian should be normalized (don't forget dx), but if you don't want to lose (signal) energy, uncomment the next line %ker = ker/sum(ker); yy(i) = y'*ker; end end

Categories : Matlab

Normal(Gaussian) Distribution Function in C++
If I got your question right you looking for the estimated normal distribution, that is for the sample mean and the variance of the sample . The former is calculated as: and the latter as: The sample mean can be used as expected value and the sample variance as in the gaussian distribution: If you want more information check out: http://mathworld.wolfram.com/SampleVariance.html http://en.wikipedia.org/wiki/Sample_mean_and_sample_covariance I hope that answered your question ;)

Categories : C++



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