Top features of linear regression in python - python

So I had to create a linear regression in python, but this dataset has over 800 columns. Is there anyway to see what columns are contributing most to the linear regression model? Thank you.

Look at the coefficients for each of the features. Ignore the sign of the coefficient:
A large absolute value means the feature is heavily contributing.
A value close to zero means the feature is not contributing much.
A value of zero means the feature is not contributing at all.

You can measure the correlation between each independent variable and dependent variable, for example:
corr(X1, Y)
corr(X2, Y)
.
.
.
corr(Xn, Y)
and you can test the model selecting the N most correlated variable.
There are more sophisticated methods to perform dimensionality reduction:
PCA (Principal Component Analysis)
(https://towardsdatascience.com/a-one-stop-shop-for-principal-component-analysis-5582fb7e0a9c)
Forward Feature Construction
Use XGBoost in order to measure feature importance for each variable and then select the N most important variables
(How to get feature importance in xgboost?)
There are many ways to perform this action and each one has pros and cons.
https://machinelearningmastery.com/dimensionality-reduction-algorithms-with-python/

If you are just looking for variables with high correlation I would just do something like this
import pandas as pd
cols = df.columns
for c in cols:
# Set this to whatever you would like
if df['Y'].corr(df[c]) > .7:
print(c, df['Y'].corr(df[c]))
after you have decided what threshold/columns you want you can append c to a list

Related

How to find appropriate clustering algorithm to cluster my data? [duplicate]

I am new to clustering algorithms. I have a movie dataset with more than 200 movies and more than 100 users. All the users rated at least one movie. A value of 1 for good, 0 for bad and blank if the annotator has no choice.
I want to cluster similar users based on their reviews with the idea that users who rated similar movies as good might also rate a movie as good which was not rated by any user in the same cluster. I used cosine similarity measure with k-means clustering. The csv file is shown below:
UserID M1 M2 M3 ............... M200
user1 1 0 0
user2 0 1 1
user3 1 1 1
.
.
.
.
user100 1 0 1
The problem i am facing is that i don't know exactly how to find most optimal number of clusters for this dataset and then draw a graph of those clusters. I am clustering them with k-means and there is no issue with that but i want to know the most stable or optimal number of clusters for this dataset.
I will appreciate some help..
Clustering is part of the unsupervised machine learning methods. Contrary to supervised methods, in unsupervised methods there is not a straightforward approach to determine the "best" model among a set of models that were trained on a certain dataset.
Nonetheless, there are some quantitative measures. Most of them are based on the concept of "how much are the points in a certain cluster more similar between themself than with the points in different clusters?" I suggest you take a look at the scikit-learn documentation on clustering evaluation. Take a look at all the techniques that do not require labels_true (i.e. at all the unsupervised techniques).
Once you have a quantitative measure about the "goodness" of a certain clustering, you usually observe how this quantity evolves while changing the number of clusters; this approach is called Elbow Method.
Here is some code that uses K-Means algorithm with all possible K values from 2 to 30, calculates various scores for each K value, and stores all scores in a DataFrame.
seed_random = 1
fitted_kmeans = {}
labels_kmeans = {}
df_scores = []
k_values_to_try = np.arange(2, 31)
for n_clusters in k_values_to_try:
#Perform clustering.
kmeans = KMeans(n_clusters=n_clusters,
random_state=seed_random,
)
labels_clusters = kmeans.fit_predict(X)
#Insert fitted model and calculated cluster labels in dictionaries,
#for further reference.
fitted_kmeans[n_clusters] = kmeans
labels_kmeans[n_clusters] = labels_clusters
#Calculate various scores, and save them for further reference.
silhouette = silhouette_score(X, labels_clusters)
ch = calinski_harabasz_score(X, labels_clusters)
db = davies_bouldin_score(X, labels_clusters)
tmp_scores = {"n_clusters": n_clusters,
"silhouette_score": silhouette,
"calinski_harabasz_score": ch,
"davies_bouldin_score": db,
}
df_scores.append(tmp_scores)
#Create a DataFrame of clustering scores, using `n_clusters` as index, for easier plotting.
df_scores = pd.DataFrame(df_scores)
df_scores.set_index("n_clusters", inplace=True)
This code assumes that all your numerical features are in a DataFrame X.
All clustering performance metrics are stored in df_scores DataFrame.
You can easily use the elbow method by plotting columns from df_scores; for instance, if you want to see the elbow graph of the Silhouette Score, you can use df_scores["silhouette_score"].plot().
It's pretty common to start with visualizing the data. Sometimes it is obvious graphically, that there are N classes/clusters. Other times you may be able to see if it's <5, <10, or <100 classes. It depends on your data really.
Another common approach is to use the Bayesian Information Criterium (BIC) or the Akaike Information Criterium (AIC).
The main takeaway is that a lot of classification-problems can yield optimal results if e.g. you have as many classes as you have inputs: every input fits perfectly in its own cluster.
BIC/AIC penalizes a high-dimensional solution, from the insight that simpler models are often better/more stable. I.e. they generalize better and overfit less.
From wikipedia:
When fitting models, it is possible to increase the likelihood by adding parameters, but doing so may result in overfitting. Both BIC and AIC attempt to resolve this problem by introducing a penalty term for the number of parameters in the model; the penalty term is larger in BIC than in AIC.
You can use the Gini index as a metric, and then do a Grid Search based on this metric. Tell me if you have any other question.
You could use the elbow method.
The base meaning of K-Means is to cluster the data points such that the total "within-cluster sum of squares (a.k.a WSS)" is minimized. Hence you can vary the k from 2 to n, while also calculating its WSS at each point; plot the graph and the curve. Find the location of the bend and that can be considered as an optimal number of clusters !

Regression analysis for linear regression

I have a regression model where my target variable (days) quantitative values ranges between 2 to 30. My RMSE is 2.5 and all the other X variables(nominal) are categorical and hence I have dummy encoded them.
I want to know what would be a good value of RMSE? I want to get something within 1-1.5 or even lesser but I am unaware what I should do to achieve the same.
Note# I have already tried feature selection and removing features will less importance.
Any ideas would be appreciated.
If your x values are categorical then it does not necessarily make much sense binding them to a uniform grid. Who's to say category A and B should be spaced apart the same as B and C. Assuming that they are will only lead to incorrect representation of your results.
As your choice of scale is the unknowns, you would be better in terms of visualisation to set your uniform x grid as being the day number and then seeing where the categories would place on the y scale if given a linear relationship.
RMS Error doesn't come into it at all if you don't have quantitative data for x and y.

Increase feature importance

I am working on a classification problem. I have around 1000 features and target variable has 2 classes. All the 1000 features have values 1 or 0. I am trying to find feature importance but my feature importance values varies from 0.0 - 0.003. I am not sure if such low value is meaningful.
Is there a way I can increase feature importance.
# Variable importance
rf = RandomForestClassifier(min_samples_split=10, random_state =1)
rf.fit(X, Y)
print ("Features sorted by their score:")
a = (list(zip(map(lambda x: round(x, 3), rf.feature_importances_), X)))
I would really appreciate any help! Thanks
Since you only have two target classes you can perform an unequal variance t-test which has been useful to find important features in a binary classification task when all other feature ranking methods have failed me. You can implement this using scipy.stats.ttest_ind function. It basically is a statistical test that checks whether the two distributions are different. if the returned p-value is less than 0.05, they can be assumed to be different distributions. To implement for each feature, follow these steps:
Extract all predictor values for class 1 and 2 respectively.
Run test_ind on these two distributions, specifying that they're variance is unknown, and make sure it's a two tailed t-test
If the p-value is less than 0.05, this feature is important.
Alternatively, you can do this for all your features and use the p-value as the measure of feature importance. The lower, the p-value, the higher the importance of a feature.
Cheers!

support vector regression time series forecasting - python

I have a dataset of peak load for a year. Its a simple two column dataset with the date and load(kWh).
I want to train it on the first 9 months and then let it predict the next three months . I can't get my head around how to implement SVR. I understand my 'y' would be predicted value in kWh but what about my X values?
Can anyone help?
given multi-variable regression, y =
Regression is a multi-dimensional separation which can be hard to visualize in ones head since it is not 3D.
The better question might be, which are consequential to the output value `y'.
Since you have the code to the loadavg in the kernel source, you can use the input parameters.
For Python (I suppose, the same way will be for R):
Collect the data in this way:
[x_i-9, x_i-8, ..., x_i] vs [x_i+1, x_i+2, x_i+3]
First vector - your input vector. Second vector - your output vector (or value if you like). Use method fit from here, for example: http://scikit-learn.org/stable/modules/generated/sklearn.svm.SVR.html#sklearn.svm.SVR.fit
You can try scaling, removing outliers, apply weights and so on. Play :)

Evaluating vector distance measures

I am working with vectors of word frequencies and trying out some of the different distance measures available in Scikit Learns Pairwise Distances. I would like to use these distances for clustering and classification.
I usually have a feature matrix of ~ 30,000 x 100. My idea was to choose a distance metric that maximizes the pairwise distances by running pairwise differences over the same dataset with the distance metrics available in Scipy (e.g. Euclidean, Cityblock, etc.) and for each metric
convert distances computed for the dataset to zscores to normalize across metrics
get the range of these zscores, i.e. the spread of the distances
use the distance metric that gives me the widest range of distances as it apparently gives me the maximum spread over my dataset and the most variance to work with. (Cf. code below)
My questions:
Does this approach make sense?
Are there other evaluation procedures that one should try? I found these papers (Gavin, Aggarwal, but they don't apply 100 % here...)
Any help is much appreciated!
My code:
matrix=np.random.uniform(0, .1, size=(10,300)) #test data set
scipy_distances=['euclidean', 'minkowski', ...] #these are the distance metrics
for d in scipy_distances: #iterate over distances
distmatrix=sklearn.metrics.pairwise.pairwise_distances(matrix, metric=d)
distzscores = scipy.stats.mstats.zscore(distmatrix, axis=0, ddof=1)
diststats=basicstatsmaker(distzscores)
range=np.ptp(distzscores, axis=0)
print "range of metric", d, np.ptp(range)
In general - this is just a heuristic, which might, or not - work. In particular, it is easy to construct a "dummy metric" which will "win" in your approach even though it is useless. Try out
class Dummy_dist:
def __init__(self):
self.cheat = True
def __call__(self, x, y):
if self.cheat:
self.cheat = False
return 1e60
else:
return 0
dummy_dist = Dummy_dist()
This will give you huuuuge spread (even with z-score normalization). Of course this is a cheating example as this is non determinsitic, but I wanted to show the basic counterexample, and of course given your data one can construct a deterministic analogon.
So what you should do? Your metric should be treated as hyperparameter of your process. You should not divide process of generating your clustering/classification into two separate phases: choosing a distance and then learning something; but you should do this jointly, consider your clustering/classification + distance pairs as a single model, thus instead of working with k-means, you will work with k-means+euclidean, k-means+minkowsky and so on. This is the only statistically supported approach. You cannot construct a method of assessing "general goodness" of the metric, as there is no such object, metric quality can be only assessed in a particular task, which involves fixing every other element (such as a clustering/classification method, particular dataset etc.). Once you perform such wide, exhaustive evaluation, check many such pairs, on many datasets, you might claim that given metric performes best in such range of tasks.

Categories