Simple linear regressions vs multiple linear regression model scaling - python-3.x

I read somewhere suggesting that in case there are multiple features(multi linear model) no feature scaling is needed because co-efficient takes care of that.
But for single feature(simple linear model); feature scaling is needed.
Is this how python scikilt learn works or I read something wrong?
Need answer from someone who has tested both with and without feature scaling in simple linear regression

Scaling is used when we want to scale the features in a particular range. In particular algorithms, the model will be sensitive to outliers so it is recommended to scale the features in a particular range. Algorithms like distance-based need feature scale. It also depends on data not in particular for any dataset such as multiple linear regression or linear regression. Sometimes features scaling is not recommended as the data points will shift from a particular range to a normal distribution range as it will lead to an impact on modelling.

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Using discretization before or after splitting data?

I am new to data mining concepts and have a question regarding implementation of a technique.
I am using the a dataset with large continuous values.
Now, I am trying to code an algorithm where I need to discretize data (not scale as it makes no impact on data along with the fact that algorithm is not a distance based one, hence no scaling needed).
Now for discretization, I have a similar question with regards to scaling and train test split.
For scaling, I know we should split data and then fit transform the train and transform the test based on what we fit from train.
But what do we do for discretization? I am using scikit learns KBinsDiscretizer and trying to make sense of whether I should split first and discretize the same way we normally scale or discretize first then scale.
The issue came up because I used the 17 bins, uniform strategy (0-16 value range)
With split then discretize, I get (0-16) range throughout in train but not in test.
With discretize and split, I get (0-16) range in both.
With former strategy, my accuracy is around 85% but with the latter, its a whopping 97% which leads me to believe I have definitely overfit the data.
Please advise on what I should be doing for discretization and whether the data interpretation was correct.

When and Whether should we normalize the ground-truth labels in the multi-task regression models?

I am trying a multi-task regression model. However, the ground-truth labels of different tasks are on different scales. Therefore, I wonder whether it is necessary to normalize the targets. Otherwise, the MSE of some large-scale tasks will be extremely bigger. The figure below is part of my overall targets. You can certainly find that columns like ASA_m2_c have much higher values than some others.
First, I have already tried some weighted loss techniques to balance the concentration of my model when it does gradient backpropagation. The result shows it didn't perform well.
Secondly, I have seen tremendous discussions regarding normalizing the input data, but hardly discovered any particular talking about normalizing the labels. It's partly because most of the people's problems are classification type and a single task. I do know pytorch provides a convenient approach to normalize the vision dataset by transform.normalize, which is still operated on the input rather than the labels.
Similar questions: https://forums.fast.ai/t/normalizing-your-dataset/49799
https://discuss.pytorch.org/t/ground-truth-label-normalization/26981/19
PyTorch - How should you normalize individual instances
Moreover, I think it might be helpful to provide some details of my model architecture. The input is first fed into a feature extractor and then several generators use the shared output representation from that extractor to predict different targets.
I've been working on a Multi-Task Learning problem where one head has an output of ~500 and another between 0 and 1.
I've tried Uncertainty Weighting but in vain. So I'd be grateful if you could give me a little clue about your studies.(If there is any progress)
Thanks.

Why does more features in a random forest decrease accuracy dramatically?

I am using sklearn's random forests module to predict values based on 50 different dimensions. When I increase the number of dimensions to 150, the accuracy of the model decreases dramatically. I would expect more data to only make the model more accurate, but more features tend to make the model less accurate.
I suspect that splitting might only be done across one dimension which means that features which are actually more important get less attention when building trees. Could this be the reason?
Yes, the additional features you have added might not have good predictive power and as random forest takes random subset of features to build individual trees, the original 50 features might have got missed out. To test this hypothesis, you can plot variable importance using sklearn.
Your model is overfitting the data.
From Wikipedia:
An overfitted model is a statistical model that contains more parameters than can be justified by the data.
https://qph.fs.quoracdn.net/main-qimg-412c8556aacf7e25b86bba63e9e67ac6-c
There are plenty of illustrations of overfitting, but for instance, this 2d plot represents the different functions that would have been learned for a binary classification task. Because the function on the right has too many parameters, it learns wrongs data patterns that don't generalize properly.

Is there any support for BiPlots when using PCA in spark.ml?

I have used kmeans and PCA to attempt to visualise high dimensional k-means clusters in two dimensions but have lost the meaning of the clusters in 2D.
Is there anyway to project the features onto to 2D plot to return some interpretability?
Any non-linear dimensionality reduction method might work better (also called "manifold learning", e.g. see sklearn's suite). The t-sne method is generally quite popular for this.
However, these do not take your cluster labels into account. If you wanted to do that (although generally you do not), you could add a penalty to the manifold learning technique that forces same-cluster points to be close together, for example.

Using SVM to perform classification on multi-dimensional time series datasets

I would like to use scikit-learn's svm.SVC() estimator to perform classification tasks on multi-dimensional time series - that is, on time series where the points in the series take values in R^d, where d > 1.
The issue with doing this is that svm.SVC() will only take ndarray objects of dimension at most 2, whereas the dimension of such a dataset would be 3. Specifically, the shape of a given dataset would be (n_samples, n_features, d).
Is there a workaround available? One simple solution would just be to reshape the dataset so that it is 2-dimensional, however I imagine this would lead to the classifier not learning from the dataset properly.
Without any further knowledge about the data reshaping is the best you can do. Feature engineering is a very manual art that depends heavily on domain knowledge.
As a rule of thumb: if you don't really know anything about the data throw in the raw data and see if it works. If you have an idea what properties of the data may be beneficial for classification, try to work it in a feature.
Say we want to classify swiping patterns on a touch screen. This closely resembles your data: We acquired many time series of such patterns by recording the 2D position every few milliseconds.
In the raw data, each time series is characterized by n_timepoints * 2 features. We can use that directly for classification. If we have additional knowledge we can use that to create additional/alternative features.
Let's assume we want to distinguish between zig-zag and wavy patterns. In that case smoothness (however that is defined) may be a very informative feature that we can add as a further column to the raw data.
On the other hand, if we want to distinguish between slow and fast patterns, the instantaneous velocity may be a good feature. However, the velocity can be computed as a simple difference along the time axis. Even linear classifiers can model this easily so it may turn out that such features, although good in principle, do not improve classification of raw data.
If you have lots and lots and lots and lots of data (say an internet full of good examples) Deep Learning neural networks can automatically learn features to some extent, but let's say this is rather advanced. In the end, most practical applications come down to try and error. See what features you can come up with and try them out in practice. And beware the overfitting gremlin.

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