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Is there any way to predict survival probability for censored objects after historical dates (prediction in future)?

I am trying to understand the possibilities and limitations of Survival analysis, in particular lifelines python package.
I fitted the Cox Proportional Hazard Model with some rossi data and got survival function showing the survival over historical period, which is clear.
Here is my code:
import pandas as pd
from lifelines.datasets import load_rossi
from lifelines import CoxPHFitter
rossi = load_rossi()
cph1 = CoxPHFitter()
cph1.fit(rossi, duration_col='week', event_col='arrest')
cph1.plot_covariate_groups('race', [0,1])
My questions are:
1. Can we somehow predict future survival probabilities of censored objects using lifelines package or any other python library for survival analysis? I mean to make survival function go beyond historical periods (e.g. probability of survival after 60 weeks?)
2. Can we use fitted model to compute survival function for new samples of data given their features values?
Regarding my 1st question I tried this (from lifelines doc):
censored_subjects = rossi.loc[~rossi['arrest'].astype(bool)]
censored_subjects_last_obs = censored_subjects['week']
# predict new survival function
cph1.predict_survival_function(censored_subjects,
conditional_after=censored_subjects_last_obs)
But it returns following 49x318 dataframe:

High frequency time series forecasting

I have a high frequency time series (observations separated by 3 seconds), which I'd like to analyse and eventually forecast short-term periods (10/20/30 min ahead) using different models. My hole dataset containing 20K observations. My goal is to come out with conclusions of how good the different models can forecast the data.
I tried first to plot the hole dataset but i couldn't identify anything :
Hole Dataset
Then I plotted only the first 500 observations and this is the result :
Firt 500 observations
I don't know why it looks just like a whitenoise !
After running the ADF test on the hole dataset it gives me a 0.0 p-value ! this means that my dataset is stationary right ?
I decided to try first the ARIMA model, from the ACF and PACF plots I can't identify p and q :
ACF
PACF
1- Is the dataset a whitenoise ? Is it possible to predict in this time series ?
2- I tried to downsample the dataset (the mean in each 4 minutes), but same think, I couldn't identify anythink, and I think this will result a loss of inforlation no ?
3- What is the length of data on which I should fit the ARIMA on the training set ? Does it make sense to use a short training set for short term forecasting period ?

Correlation between two dataframes / curves

I have yield curve data for two currencies (Euro and U.S. Dollar). For each of these currencies I have 16 variables (16 maturities). I have generated, using some model, synthetic curves and I want to relate the curves of the two currencies. That is, what is the correlation between the two currencies? I am asking this question as my model should capture this correlation. For example, it wouldn't be great if a 4% euro curve is generated and at the same time a -4% level curve is generated for the dollar. How can I do this? I don't like a correlation matrix as this yields a 16x16 matrix per model (I have multiple). Any thoughts?! Could be very helpful.

Just build a new DataFrame out of the two other DataFrames with the Series you want and call corr?
It is hard to provide a exact solution (and i may not understand your problem fully), as you didn't provide any information on how the data looks or what your code looks already
import pandas as pd
# your code so far...
df_corr = pd.DataFrame()
df_corr['eur_curve'] = df_eur # asumming you have a df_eur with the curve and 16 "variables"
df_corr['usd_cuve'] = df_usd # asumming you have a df_usd with the curve and 16 "variables"
corr = df_corr.corr()

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 !

How do I denormalize the sklearn diabetes dataset?

There is a nice example of linear regression in sklearn using a diabetes dataset.
I copied the notebook version and played with it a bit in Jupyterlab. Of course, it works just like the example. But I wondered what I was really seeing.
There is a chart with unlabeled axes.
I wondered what the label (dependent variable) was.
I wondered which of the 10 independent variables was being used.
So I played around with the nice features provided by ipython/jupyter:
diabetes.DESCR
Diabetes dataset
================
Notes
-----
Ten baseline variables, age, sex, body mass index, average blood
pressure, and six blood serum measurements were obtained for each of
n = 442 diabetes patients, as well as the response of interest, a
quantitative measure of disease progression one year after baseline.
Data Set Characteristics:
:Number of Instances: 442
:Number of Attributes: First 10 columns are numeric predictive values
:Target: Column 11 is a quantitative measure of disease progression one year after baseline
:Attributes:
:Age:
:Sex:
:Body mass index:
:Average blood pressure:
:S1:
:S2:
:S3:
:S4:
:S5:
:S6:
Note: Each of these 10 feature variables have been mean centered and scaled by the standard
deviation times `n_samples` (i.e. the sum of squares of each column totals 1).
Source URL:
http://www4.stat.ncsu.edu/~boos/var.select/diabetes.html
For more information see:
Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani (2004)
"Least Angle Regression," Annals of Statistics (with discussion), 407-499.
(http://web.stanford.edu/~hastie/Papers/LARS/LeastAngle_2002.pdf)'
From the Source URL, we are led to the original raw data which is a tab-separated unnormalized copy of the data. It also further explains what the "S" features were in the problem domain.
Interestingly, sex was one of [1,2] with a guess as to what they meant.
But my real question is whether there is a way within sklearn to determine
how to denormalize the data in sklearn?
Is there a way to denormalize the coefficients and intercept so that one could
express the fit algebraically?
or is this just a demonstration of linear regression?

There is no way to denormalize data without any information about the data prior to the normalization. However, note that the sklearn.preprocessing classes MinMaxScaler, StandardScaler, etc. do include inverse_transform methods (example), so if this were also provided in the example it would be easy to do. As it stands, as you say, this is just a regression demonstration.