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Probabilistic Graphical Models (PGMs) are: Connectionist: RBMs are PGMs and neural networks (source) Bayesian: Bayes Networks are bayesian (Wikipedia article) Symbolist: Markov Logic Networks (source) Analogizers and Evolutionaries: According to Domingos, they are also in Markov Logic Networks. So the answer is that you can't simply categorize such a ...


6

It means that your hyperparameter space is tree-like: the value chosen for one hyperparameter determines what hyperparameter will be chosen next and what values are available for it. From a HyperOpt example, in which the model type is chosen first, and depending on that different hyperparameters are available: space = hp.choice('classifier_type', [ { '...


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Efficient use of resources It is a balancing game with the learning rate, and one reason you don't normally see people do this is that you want to utilise as much of the GPU as possible. It is commonly preferred to start with the maximum batch size you can fit in memory, then increase the learning rate accordingly. This applies to "effective batch sizes&...


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There are different flavors of Naive Bayes, so the answer depends a bit on the use case. One potential issue with outliers is that unseen observations can lead to 0 probabilities. For example, Bernoulli Naive Bayes applied to word features will always produce 0 probabilities when it encounters a word that wasn't seen in the training data. Outliers in this ...


4

Likelihood-ratio tests are a mainstay of classical hypothesis testing. The idea is to form the likelihoods of the two hypotheses under consideration, and choose the one with the highest likelihood if their ratio is sufficiently large. Hypotheses come in two flavors: simple, and composite. Simple tests are those for which the hypothesis uniquely defines the ...


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All of the answers here, including the accepted one, are conspicuously confused. I down-voted the accepted answer but downvotes of users who lack reputation in this "community" are not counted. I have a reputation of more than 200,000 (two-hundred-thousand) on math.stackexchange.com and I have a Ph.D. in statistics, but none of that counts here. The ...


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I do not think your formulation is correct. What you have described are just conditional distributions for each word in the sentence but not the joint conditional distribution, given a specific class. In your case, we have by Bayes rule: $$ Pr(spam | X) \propto Pr(X | spam) \times Pr(spam) = Pr(you, won, lottery, for, 1million | spam) \times Pr(spam).$$ ...


4

First of all you might want to know there is a "new" Keras tuner, which includes BayesianOptimization, so building an LSTM with keras and optimizing its hyperparams is completely a plug-in task with keras tuner :) You can find a recent answer I posted about tuning an LSTM for time series with keras tuner here So, 2 points I would consider: I would not loop ...


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The Bayesian approach should be used in the case of: Strong priors - You have preexisting data and / or domain knowledge that you want to incorporate into the analysis. Distributional estimates - Instead of point estimates, the result of Bayesian analysis will yield distributions. Those distributions will better quantify the uncertainty of predictions. In ...


3

No, it's not problematic. Most data scientists do not need or use deep learning. Deep learning is very popular right now, but that does not mean it's widely used. Deep learning can lead to substantial overfitting on small to medium datasets (I'm arbitrarily going to say that means less than 2 GB), which are the sizes that most people have. Deep learning is ...


3

In short The problem assumes a uniform prior distribution function. All possible $P(H)$ are equally likely. Because they are standardizing the probability distribution function at the end it does not matter what value is placed in prior=np.repeat(1,grid_points) Likelihood function The likelihood function answers the question, how probable is the prior ...


3

Your intuition about 'no effect' is true in some sense. But this replacement may be not the best use of the information you have. The choice of missing value treatment depends on your initial problem statement. In all the cases I assume that you have already somehow estimated conditional means $\mu_0$ and $\mu_1$ and the common variance matrix $S$. ...


3

As mentioned in that Kaggle notebook, you can use it pretty much as just a drop-in replacement for other search methods (grid or random). Bayesian searches still are random searches over a predefined search space/distribution, but now the algorithm pays attention to how well hyperparameter combinations perform, and will put more emphasis on high-performing ...


3

My understanding is: The first line is OK - it derives from Bayes Rule Assume that this probability follows a logistic function, that is that $$P(C_1|x) = \frac{1}{1+exp(-a)}$$ Then if $$ y = \frac{1}{1+exp(-z)}$$ then $$ z = ln(\frac{y}{1-y})$$ (some lines below but with $a$ and $\sigma$) Therefore: $$ a = ln(\frac{P(C_1|x)}{1-P(C_1|x)})$$ If there ...


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I'll try and provide some intuition for you here, instead of focusing on the mechanics of the math behind the methods. Imagine you are evaluating whether a coin is fair or not, so you collect a sequence of heads and tails as your data set. In MLE, we simply look at the data we collected and find the maximum likelihood... this works well when we have no prior ...


2

Based on this paper (Qi, Szummer, and Minka. 2005. Bayesian Conditional Random Fields): In this paper, we propose Bayesian Conditional Random Fields (BCRF), a novel Bayesian approach to training and inference for conditional random fields We can see that the original CRF model is presumably not Bayesian, since this paper's contribution is a novel ...


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Only Domingos knows for sure, since he invented this taxonomy, but I'd guess it would fall under "connectionists" (which he associates with neural networks), since graphs are all about connections (between random variables). Bayesians would be my second choice. CRFs are not natively Bayesian (you don't use priors or posteriors of the model parameters), but ...


2

Ensemble learning is categorized into 4 different classes: bagging, boosting, stacking, hierarchy classification and sometimes they consider grading as another category. Each one of these categories has many different types. For example, in boosting you have Adaboost, Gboost and many others. It is very important to understand the differences between these ...


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It is a 49 page long paper, so following observations are based only on a cursory reading. The optimisation is for finding best value of parameters for cost function of machine learning models. Rather than finding a fixed value of the parameters, it is assumed that the parameters come from statistical distribution and the task is to find the nature/shape of ...


2

Let $A$, $B$, $C$ be three (potentially dependent) events. By the probability chain rule: $$ P(A,B,C)=P(A|B,C)P(B,C)=P(A|B,C)P(B|C)P(C) $$ So we can do \begin{align} P(A|B,C) &= \frac{ P(A,B,C)}{P(B|C)P(C)} \\ &= \frac{ P(B,C|A) P(A) }{ P(B|C)P(C) } \\ &= \frac{ P(B|A,C) P(A) P(C) }{ P(B|C)P(C) } \\ &= \frac{ P(B|A,C) P(A) }{ P(B|C) } \end{...


2

Your interpretation of L1 regularization sounds right. Is it used to perform feature selection? Yes, in the broad sense that this 'encourages' coefficients in the linear model to be 0, and those features with 0 coefficients are not used and can be removed. Of course, this assumption about the prior distribution of coefficients is just an assumption you're ...


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Likelihood and probability are two very different concepts: One talk about probabilities when the distribution is already known and one want to know how probable an event is. Likelihood on the other hand is usually much more experimental. It is used when, given some results, one want to know how likely it is that those results fit a specific distribution. ...


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It actually makes perfect sense to use both. Gal et al. provided a nice theory on how to interpret dropout through a Bayesian lense. In a nutshell, if you use dropout + regularization you are implicitly minimizing the same loss as for a Bayesian Neural Network (BNN), where you learn the posterior distribution over the network weights given the training data. ...


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I don't know if that is the case, but if some kind of continuity assumptions are realistic, you could try to move away from categorical variables (block) to continuous variables (longitude and latitude). Then, if you have information on two neighboring blocks, you could interpolate those values with say a spline. Of course, this can also be fitted into a ...


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One option is to move to a more rigorous geographic information system (GIS) data structure. For example, both plus codes and H3 are designed for nested location data. If your data is reformated to either system, you can easily choose the level of precision for aggregating location data.


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The reasoning will be: "The more data for training the better". Then you have to keep in mind that the validation/hold-out set has to resemble how it should work on production/testing. The theory is that the larger the training data, the better the model should generalize. The validation set can be much smaller, on extremely big dataset you can ...


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This may be an unpopular opinion to some, but in my experience Bayesian statistics is not particularly useful in data science in industry, for a couple of reasons: A Bayesian approach is very useful when our questions are about statistical inference. However, in data science, more often than not, we are dealing with prediction. There may be some situations ...


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Perhaps I am missing something, but isn't it as follows? Probability of drawing a lever from a specific machine value $p\left(M_1\right)$ 10/100 $p\left(M_2\right)$ 25/100 $p\left(M_3\right)$ 25/100 $p\left(M_4\right)$ 40/100 And Probability of faulty lever given machine value $p\left(F|M_1\right)$ 10/100 $p\left(F|M_2\right)$ 15/100 $p\left(F|M_3\...


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From a bayesian perspective, I would not begin the answer talking about the regularization term. I would rather say what is the prior distribution you are assuming (since this is the starting point in the bayesian framework) and then the regularization term comes up as a consequence, after calculating the log-posterior. Also, I believe that feature ...


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It is possible to predict a single value from a Bayesian Neural Network. Given a set of input data, conduct the forward pass to generate the resulting probability distribution. Then convert that probability distribution to a single specific value in one of the following common ways: Sample - Take a random sample. That random sample will automatically be ...


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