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How to add training data to the model after initial training?

I am trying to add data for my scikit-learn model after it has already been trained. For example, I have the data that I used in the beginning (there are about 250 of them). After that, I need to train this model one more time by calling the function, and so on. The only thing that came to my mind was to add new values ​​to the existing data array every time and train the model again, but this is very resource-intensive and takes more time.
Is there another way to train the machine learning model?
model = LinearRegression().fit(test, result)
reg.predict(task)
### and here I want to add some data, for example one or two examples like:
model.addFit(one_test, one_result)

The short answer in your case (using the sklearn.linear_model.LinearRegression model) is no, it is not possible to add one or two more examples and train without adding this to the original training set and fitting it all at the same time. Under the hood, the model is simply using Ordinary Least Squares (described here) which requires the complete matrix of training data on which to fit your model. However, this algorithm is very fast and in the case of ~ hundreds of training examples, it would be very quick to re-calculate the parameters of the model with each new couple examples.

In Leave One Out Cross Validation, How can I Use `shap.Explainer()` Function to Explain a Machine Learning Model?

Background of the Problem
I want to explain the outcome of machine learning (ML) models using SHapley Additive exPlanations (SHAP) which is implemented in the shap library of Python. As a parameter of the function shap.Explainer(), I need to pass an ML model (e.g. XGBRegressor()). However, in each iteration of the Leave One Out Cross Validation (LOOCV), the ML model will be different as in each iteration, I am training on a different dataset (1 participant’s data will be different). Also, the model will be different as I am doing feature selection in each iteration.
Then, My Question
In LOOCV, How can I use shap.Explainer() function of shap library to present the performance of a machine learning model? It can be noted that I have checked several tutorials (e.g. this one, this one) and also several questions (e.g. this one) of SO. But I failed to find the answer of the problem.
Thanks for reading!
Update
I know that in LOOCV, the model found in each iteration can be explained by shap.Explainer(). However, as there is 250 participants' data, if I apply shap here for each model, there will be 250 output! Thus, I want to get a single output which will present the performance of the 250 models.

You seem to train model on a 250 datapoints while doing LOOCV. This is about choosing a model with hyperparams that will ensure best generalization ability.
Model explanation is different from training in that you don't sift through different sets of hyperparams -- note, 250 LOOCV is already overkill. Will you do that with 250'000 rows? -- you are rather trying to understand which features influence output in what direction and by how much.
Training has it's own limitations (availability of data, if new data resembles the data the model was trained on, if the model good enough to pick up peculiarities of data and generalize well etc), but don't overestimate explanation exercise either. It's still an attempt to understand how inputs influence outputs. You may be willing to average 250 different matrices of SHAP values. But do you expect the result to be much more different from a single random train/test split?
Note as well:
However, in each iteration of the Leave One Out Cross Validation (LOOCV), the ML model will be different as in each iteration, I am training on a different dataset (1 participant’s data will be different).
In each iteration of LOOCV the model is still the same (same features, hyperparams may be different, depending on your definition of iteration). It's still the same dataset (same features)
Also, the model will be different as I am doing feature selection in each iteration.
Doesn't matter. Feed resulting model to SHAP explainer and you'll get what you want.

Averaging linear separators obtained from SVM

For research purposes, I find myself needing to traing SVM via SGD on a large DS (that is, a large number of examples). This makes using scikit-learn's implementation (SGDClassifier) problematic, as it requires loading the entire DS at once.
The algorithm I am familiar with uses n step of SGD to obtain n different separators w_i, and then averages them (specifics can be seen in slide 12 of https://www.cse.huji.ac.il/~shais/Lectures2014/lecture8.pdf).
This made me think that maybe I can use scikit-learn to train multiple such classifiers and then take the average of the resulting linear separators (assume no bias).
Is this a reasonable line of thinking, or does scikit-learn's implementation not fall under my logic?
Edit: I am well aware of the alternatives for training SVM in different ways, but this is for a specific research purpose. I would just like to know if this line of thinking is possible with scikit-learn's implementation, or if you are aware of an alternative that will allow me to train SVM using SGD without loading an entire DS to memory.

SGDClassifier have a partial_fit method, and one of the primary objectives of partial_fit method is to scale sklearn models to large-scale datasets. Using this, you can load a part of the dataset into RAM, feed it to SGD, and keep repeating this unless full dataset is used.
In code below, I use KFold mainly to imitate loading chunk of dataset.
class GD_SVM(BaseEstimator, ClassifierMixin):
def __init__(self):
self.sgd = SGDClassifier(loss='hinge',random_state=42,fit_intercept=True,l1_ratio=0,tol=.001)
def fit(self,X,y):
cv = KFold(n_splits=10,random_state=42,shuffle=True)
for _,test_id in cv.split(X,y):
xt,yt = X[test_id],y[test_id]
self.sgd = self.sgd.partial_fit(xt,yt,classes=np.unique(y))
def predict(self,X):
return self.sgd.predict(X)
To test this against regular (linear) SVM:
X,y = load_breast_cancer(return_X_y=True)
X = StandardScaler().fit_transform(X) #For simplicity, Pipeline is better choice
cv = RepeatedStratifiedKFold(n_splits=5,n_repeats=5,random_state=43)
sgd = GD_SVM()
svm = LinearSVC(loss='hinge',max_iter=1,random_state=42,
C=1.0,fit_intercept=True,tol=.001)
r = cross_val_score(sgd,X,y,cv=cv) #cross_val_score(svm,X,y,cv=cv)
print(r.mean())
This returned 95% accuracy for above GD_SVM, and 96% for SVM. In Digits dataset SVM had 93% accuracy, while GD_SVM had 91%. While these performances are broadly similar, as these measurements show, please note that they are not identical. This is expected, since these algorithms use pretty different optimization algorithms, but I think careful tuning of hyper-parameter would reduce the gap.

Based on the concern of loading all of the data in memory, if you have access to more compute resources, you may want to use PySpark's SVM implementation: https://spark.apache.org/docs/2.2.0/ml-classification-regression.html#linear-support-vector-machine, as that Spark is built for large scale data processing. I don't know if averaging the separators from multiple Scikit-Learn models would work as expected; there isn't a clean way to instantiate a new model with new separators, based on the documentation (https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html), so it would probably have to be implemented as an ensemble approach.

If you insist on using the whole DS for training instead of sampling (btw that is what the slides describe) and you do not care about performance, I would train n classifiers, and then select only their support vectors and retrain final version on those support vectors only. This way you effectively dismiss most of the data and concentrate only on the points that are important for the classification.

Linear regression: Good results for training data, horrible for test data

I am working with a dataset of about 400.000 x 250.
I have a problem with the model yielding a very good R^2 score when testing it on the training set, but extremely poorly when used on the test set. Initially, this sounds like overfitting. But the data is split into training/test set at random and the data set i pretty big, so I feel like there has to be something else.
Any suggestions?
Splitting dataset into training set and test set
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(df.drop(['SalePrice'],
axis=1), df.SalePrice, test_size = 0.3)
Sklearn's Linear Regression estimator
from sklearn import linear_model
linReg = linear_model.LinearRegression() # Create linear regression object
linReg.fit(X_train, y_train) # Train the model using the training sets
# Predict from training set
y_train_linreg = linReg.predict(X_train)
# Predict from test set
y_pred_linreg = linReg.predict(X_test)
Metric calculation
from sklearn import metrics
metrics.r2_score(y_train, y_train_linreg)
metrics.r2_score(y_test, y_pred_linreg)
R^2 score when testing on training set: 0,64
R^2 score when testing on testing set: -10^23 (approximatly)

While I agree with Mihai that your problem definitely looks like overfitting, I don't necessarily agree on his answer that neural network would solve your problem; at least, not out of the box. By themselves, neural networks overfit more, not less, than linear models. You need somehow to take care of your data, hardly any model can do that for you. A few options that you might consider (apologies, I cannot be more precise without looking at the dataset):
Easiest thing, use regularization. 400k rows is a lot, but with 250 dimensions you can overfit almost whatever you like. So try replacing LinearRegression by Ridge or Lasso (or Elastic Net or whatever). See http://scikit-learn.org/stable/modules/linear_model.html (Lasso has the advantage of discarding features for you, see next point)
Especially if you want to go outside of linear models (and you probably should), it's advisable to first reduce the dimension of the problem, as I said 250 is a lot. Try using some of the Feature selection techniques here: http://scikit-learn.org/stable/modules/feature_selection.html
Probably most importantly than anything else, you should consider adapting your input data. The very first thing I'd try is, assuming you are really trying to predict a price as your code implies, to replace it by its logarithm, or log(1+x). Otherwise linear regression will try very very hard to fit that single object that was sold for 1 Million $ ignoring everything below $1k. Just as important, check if you have any non-numeric (categorical) columns and keep them only if you need them, in case reducing them to macro-categories: a categorical column with 1000 possible values will increase your problem dimension by 1000, making it an assured overfit. A single column with a unique categorical data for each input (e.g. buyer name) will lead you straight to perfect overfitting.
After all this (cleaning data, reducing dimension via either one of the methods above or just Lasso regression until you get to certainly less than dim 100, possibly less than 20 - and remember that this includes any categorical data!), you should consider non-linear methods to further improve your results - but that's useless until your linear model provides you at least some mildly positive R^2 value on test data. sklearn provides a lot of them: http://scikit-learn.org/stable/modules/kernel_ridge.html is the easiest to use out-of-the-box (also does regularization), but it might be too slow to use in your case (you should first try this, and any of the following, on a subset of your data, say 1000 rows once you've selected only 10 or 20 features and see how slow that is). http://scikit-learn.org/stable/modules/svm.html#regression have many different flavours, but I think all but the linear one would be too slow. Sticking to linear things, http://scikit-learn.org/stable/modules/sgd.html#regression is probably the fastest, and would be how I'd train a linear model on this many samples. Going truly out of linear, the easiest techniques would probably include some kind of trees, either directly http://scikit-learn.org/stable/modules/tree.html#regression (but that's an almost-certain overfit) or, better, using some ensemble technique (random forests http://scikit-learn.org/stable/modules/ensemble.html#forests-of-randomized-trees are the typical go-to algorithm, gradient boosting http://scikit-learn.org/stable/modules/ensemble.html#gradient-tree-boosting sometimes works better). Finally, state-of-the-art results are indeed generally obtained via neural networks, see e.g. http://scikit-learn.org/stable/modules/neural_networks_supervised.html but for these methods sklearn is generally not the right answer and you should take a look at dedicated environments (TensorFlow, Caffe, PyTorch, etc.)... however if you're not familiar with those it is certainly not worth the trouble!

Break up Random forest classification fit into pieces in python?

I have almost 900,000 rows of information that I want to run through scikit-learn's Random Forest Classifier algorithm. Problem is, when I try to create the model my computer freezes completely, so what I want to try is running the model every 50,000 rows but I'm not sure if this is possible.
So the code I have now is
# This code freezes my computer
rfc.fit(X,Y)
#what I want is
model = rfc.fit(X.ix[0:50000],Y.ix[0:50000])
model = rfc.fit(X.ix[0:100000],Y.ix[0:100000])
model = rfc.fit(X.ix[0:150000],Y.ix[0:150000])
#... and so on

Feel free to correct me if I'm wrong, but I assume you're not using the most current version of scikit-learn (0.16.1 as of writing this), that you're on a Windows machine and using n_jobs=-1 (or a combination of all three). So my suggestion would be to first upgrade scikit-learn or set n_jobs=1 and try fitting on the whole dataset.
If that fails, take a look at the warm_start parameter. By setting it to True and gradually incrementing n_estimators you can fit additional trees on subsets of your data:
# First build 100 trees on the first chunk
clf = RandomForestClassifier(n_estimators=100, warm_start=True)
clf.fit(X.ix[0:50000],Y.ix[0:50000])
# add another 100 estimators on chunk 2
clf.set_params(n_estimators=200)
clf.fit(X.ix[0:100000],Y.ix[0:100000])
# and so forth...
clf.set_params(n_estimators=300)
clf.fit(X.ix[0:150000],Y.ix[0:150000])
Another possibility is to fit a new classifier on each chunk and then simply average the predictions from all classifiers or merging the trees into one big random forest like described here.

Another method similar to the one linked in Andreus' answer is to grow the trees in the forest individually.
I did this a while back: basically I trained a number of DecisionTreeClassifier's one at a time on different partitions of the training data. I saved each model via pickling, and afterwards I loaded them into a list which was assigned to the estimators_ attribute of a RandomForestClassifier object. You also have to take care to set the rest of the RandomForestClassifier attributes appropriately.
I ran into memory issues when I built all the trees in a single python script. If you use this method and run into that issue, there's a work-around, I posted in the linked question.

from sklearn.datasets import load_iris
boston = load_iris()
X, y = boston.data, boston.target
### RandomForestClassifier
from sklearn.ensemble import RandomForestClassifier
rfc = RandomForestClassifier(n_estimators=10, warm_start=True)
rfc.fit(X[:50], y[:50])
print(rfc.score(X, y))
rfc.n_estimators += 10
rfc.fit(X[51:100], y[51:100])
print(rfc.score(X, y))
rfc.n_estimators += 10
rfc.fit(X[101:150], y[101:150])
print(rfc.score(X, y))
Below is differentiation between warm_start and partial_fit.
When fitting an estimator repeatedly on the same dataset, but for multiple parameter values (such as to find the value maximizing performance as in grid search), it may be possible to reuse aspects of the model learnt from the previous parameter value, saving time. When warm_start is true, the existing fitted model attributes an are used to initialise the new model in a subsequent call to fit.
Note that this is only applicable for some models and some parameters, and even some orders of parameter values. For example, warm_start may be used when building random forests to add more trees to the forest (increasing n_estimators) but not to reduce their number.
partial_fit also retains the model between calls, but differs: with warm_start the parameters change and the data is (more-or-less) constant across calls to fit; with partial_fit, the mini-batch of data changes and model parameters stay fixed.
There are cases where you want to use warm_start to fit on different, but closely related data. For example, one may initially fit to a subset of the data, then fine-tune the parameter search on the full dataset. For classification, all data in a sequence of warm_start calls to fit must include samples from each class.

Some algorithms in scikit-learn implement 'partial_fit()' methods, which is what you are looking for. There are random forest algorithms that do this, however, I believe the scikit-learn algorithm is not such an algorithm.
However, this question and answer may have a workaround that would work for you. You can train forests on different subsets, and assemble a really big forest at the end:
Combining random forest models in scikit learn