I have financial data with values like: "Volume", "Profit/Loss", "Cost", etc
Now, it is safe to assume that every record in this data set is a "realization" or outcome of a single random variable, hence we may model this dataset as a set of iid random variables.
Now, I want to leverage this data set to model the underlying distribution of this random variable.
Can anyone point me in the right direction?
If you like a Bayesian approach and programming in Python, I can recommend PyMC3 and the book Bayesian Methods for Hackers. Chapter 1 talks you through how to estimate a random variable from some data using this library.
Related
I am following a course on udemy about data science with python.
The course is focused on the output of the algorithm and less on the algorithm by itself.
In particular I am performing a decision tree. Every doing I run the algorithm on python, also with the same samples, the algorithm gives me a slightly different decision tree. I have asked to the tutors and they told me "The decision trees does not guarantee the same results each run because of its nature." Someone can explain me why more in detail or maybe give me an advice for a good book about it?
I did the decision tree of my data importing:
import numpy as np
import pandas as pd
from sklearn import tree
and doing this command:
clf = tree.DecisionTreeClassifier()
clf = clf.fit(X,y)
where X are my feature data and y is my target data
Thank you
The DecisionTreeClassifier() function is apparently documented here:
https://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeClassifier.html
So this function has many arguments. But in Python, function arguments may have default values. Here, all arguments have default values, so you can even call the function with an empty argument list, like this:
clf = tree.DecisionTreeClassifier()
The parameter of interest, random_state is documented like this:
random_state: int, RandomState instance or None, default=None
So your call is equivalent to, among many other things:
clf = tree.DecisionTreeClassifier(random_state=None)
The None value tells the library that you don't want to bother with providing a seed (that is, an initial state) to the underlying pseudo-random number generator. Hence, the library has to come up with some seed.
Typically, it will take the current time value, with microsecond precision if possible, and apply some hash function. So at every call you will get a different initial state, and so a different sequence of pseudo-random numbers. Hence, a different tree.
You might want to try forcing the seed. For example:
clf = tree.DecisionTreeClassifier(random_state=42)
and see if your problem persists.
Now, regarding why does the decision tree require pseudo-random numbers, this is discussed for example here:
According to scikit-learn’s “best” and “random” implementation [4], both the “best” splitter and the “random” splitter uses Fisher-Yates-based algorithm to compute a permutation of the features array.
The Fisher-Yates algorithm is the most common way to compute a random permutation. Also, if stopped before completion, it can be used to extract a random subset of the data sample, for example if you need a random 10% of the sample to be excluded from the data fitting and set aside for a later cross-validation step.
Side note: in some circumstances, non-reproducibility can become a pain point, for example if you want to study the influence of an external parameter, say some global Y values bias. In that case, you don't want uncontrolled changes in the random numbers to blur the effects of your parameter changes. Hence the need for the API to provide some way to control the seed value.
I am trying to use hmmlearn's GaussianHMM to fit a Hidden Markov Model with 2 main states, while allowing for multiple exogenous variables. My goal is to determine two states of GDP growth (one with low variance and the other with high variance), these states then depend on lagged unemployment, lagged commercial confidence level etc. I have a couple of questions:
Using hmmlearn's GaussiansHMM, I have read through the documentation but I cannot find any mention of exogenous variable. Using the method fit(X, lengths=None), I see that X can have n_features columns, do I understand correctly that I should pass in an array with the first column being the endogenous varible (GDP growth in my case) and the rest of columns are the exogenous variables ?
Is hmmlearn's GaussianHMM equivalent to statsmodels.tsa.regime_switching.markov_regression.MarkovRegression ? This model allows for exog_tvtp which means that exogenous variables are used to calculate a time varying transition probabilities matrix.
An example of fitting the monthly returns of the S&P500, no exogenous variable.
import numpy as np
import pandas as pd
from hmmlearn.hmm import GaussianHMM
import yfinance as yf
sp500 = yf.download("^GSPC")["Adj Close"]
# Fitting an absolute return model because we only care about volatility #
rets = np.log(sp500/sp500.shift(1)).dropna()
rets.index = pd.to_datetime(rets.index)
rets = rets.resample("M").sum()
model = GaussianHMM(n_components=2)
model.fit(rets.to_frame())
state_sequence = model.predict(rets.to_frame())
Imagine if I want to add a dependency on exogenous variables to the returns of the S&P500, for example on economic growth or past volatilities, is there a way to do this ?
Thanks for any help.
n_features can be thought of as the temporal domain, and should not be conflated with features that describe the complexity of ie. a regression model.
If your hidden states are the two states of GDP growth, then the observed variable (or emissions) that you are trying to infer the hidden states from should be the feature space (a.k.a. n_features).
This should be a single measurement (emission) descriptive of a combination of your "exogenous variables", collected over time. hmmlearn will not be able to take multivariate emissions.
Suggestions
If I understand your question correctly, perhaps what you might be looking for are Kalman filters. KF produces estimates of unknowns based on multiple measurements (ie. all of your exogenous variables) that ultimately produce a model more accurate than those based on a single measurement.
If you wish each hidden state to have multiple independent emissions then what you might be looking for is a structured perceptron. This is discussed here: Hidden Markov Model for multiple observed variables
I want to construct a LightGBM Dataset object from very large X and y, which can not be load to memory. Is there any method that can construct Dataset in "batch"? eg. something like
import lightgbm as lgb
ds = lgb.Dataset()
for X, y in data_generator():
ds.add_new_data(data=X, label=y)
regarding the data there are a few hacks, for example, if your data has numeric, you make sure the precision are too long, e.g. probably two digits would be enough (it depends on your data). or if you have categorical data make sure you store them with digits. but probably you are looking for a better approach
There is a concept called incremental learning. Basically you make a model (a tree) in your first iteration using the first batch of data. Then for your next model, you use that tree as a template and only updates the values (you can also allow for shrinkage). you can use the keep_training_booster for such scenario and please read on your own to learn the mechanism.
The third technique is you make multiple models: say you divide your data into N pieces and make N models, then use an ensemble approach. This way you have used your entire data with N number of observations.
I'm trying to calculate performance in a different way how it is built in for models right now.
I would like to access raw predictions during cross-validation, so I can calculate performance on my own.
g = h2o.get_grid(grid_id)
for m in g.models:
print "Model %s" % m.model_id
rrc[m.model_id] = m.cross_validation_holdout_predictions()
I could just run prediction with a model on my dataset, but I think then this test might be biased because the model has seen this data before, or not? Can I take new predictions made on the same data set and use it to calculate performance?
I would like to access raw predictions during cross-validation, so I can calculate performance on my own.
If you want to calculate a custom metric on the cross-validated predictions, then set keep_cross_validation_predictions = True and you can access the raw predicted values using the .cross_validation_holdout_predictions() method like you have above.
Can I take new predictions made on the same data set and use it to calculate performance?
It sounds like you're asking if you can use only training data to estimate model performance? Yes, using cross-validation. If you set nfolds > 1, H2O will do cross-validation and compute a handful of cross-validated performance metrics for you. Also, if you tell H2O to save the cross-validated predictions, you can compute "cross-validated metrics" of your own.
I'm trying to understand bayesian network. I have a data file which has 10 attributes, I want to acquire the confusion table of this data table ,I thought I need to calculate tp,fp, fn, tn of all fields. Is it true ? if it's then what i need to do for bayesian network.
Really need some guidance, I'm lost.
The process usually goes like this:
You have some labeled data instances
which you want to use to train a
classifier, so that it can predict
the class of new unlabeled instances.
Using your classifier
of choice (neural networks, bayes
net, SVM, etc...) we build a
model with your training data
as input.
At this point, you usually would like
to evaluate the performance of the
model before deploying it. So using a
previously unused subset of the data
(test set), we compare the model
classification for these instances
against that of the actual class. A
good way to summarize these results
is by a confusion matrix which shows
how each class of instances is
predicted.
For binary classification tasks, the convention is to assign one class as positive, and the other as negative. Thus from the confusion matrix, the percentage of positive instances that are correctly classified as positive is know as the True Positive (TP) rate. The other definitions follows the same convention...
Confusion matrix is used to evaluate the performance of a classifier, any classifier.
What you are asking is a confusion matrix with more than two classes.
Here is the steps how you do:
Build a classifier for each class, where the training set consists of
the set of documents in the class (positive labels) and its
complement (negative labels).
Given the test document, apply each classifier separately.
Assign the document to the class with the maximum score, the
maximum confidence value, or the maximum probability
Here is the reference for the paper you can have more information:
Picca, Davide, Benoît Curdy, and François Bavaud.2006.Non-linear correspondence analysis in text retrieval: A kernel view. In Proc. JADT.