There are many ML techniques to estimate latent variables such as the EM algorithm. Is there a technique that allows for thresholds for each of the latent variables? I have a feature space with 10 variables $(X_1,\dots,X_{10})$ and the outcome $Y$. 7 of the $X$ features are known (I have their observations) and 3 are unknown. Each of the unknown can be within a range from 0 up to a positive constant number. What ML technique would you recommend for …
Based on the deeplearningbook: $$MSE = E[(\theta_m^{-} - \theta)^2]$$ $$equals$$ $$Bias(\theta_m^{-})^2 + Var(\theta_m^{-})$$ where m is the number of samples in training set, $\theta$ is the actual parameter in the training set and $\theta_m^{-}$ is the estimated parameter. I can't get to the second equation. Further, I don't understand how the first expression is gained. Note: $Bias(\theta_m^{-})^2 = E(\theta_m^{-2}) - \theta^2$ Also how bias and variance evaluated in classification.?
I was wondering, would it be correct to say, when we treat two variances of two populations as a random variable itself (or as a score), that we can simply get a resultant variance V_subtract = V_pop1 - V_pop2 (e.g. V_subtract = (1-0.5) = 0.5. If so, I am wondering what that says about the actual standard error in terms of this subtracted variance score, if we know the total sample size of population 1 and population 2 respectively which …
I wrote a program to find the best combination of coefficients to describe a variable. However, the coefficients from the gridsearchcv do not match well with the expected line. This is a sample of my data: pipe = make_pipeline(process, SelectKBest(f_regression), model) gs=GridSearchCV(pipe,params,n_jobs=-1,cv=5, return_train_score = False); gs.fit(x_train, y_train) fin = gs.best_estimator_.steps[2][1]; coef = fin.coef_; intercept = fin.intercept_ and these are the coefficients given: Then if I plot the line with the coefficients: xplot = 16.15589 + 1.13934372*df_loc.ChargeAmount + 1.605411*df_loc.PatientPrice + 6.81365603*df_loc.LastCost …
I'm working with several estimators of all kind. Then, I want to stack these estimators, and the best is if they have low correlation between them. I suppose that the correlation method depends on the type of dependent variable, if it's categorical or numerical. In my case, it's categorical, and the estimators are classifiers. How can I do the correlation between two estimators?
Context: My team and I are working on a RL problem for a specific application. We have data collected from user interactions (states, actions, etc.). It is too costly for us to emulate agents. We decided therefore to concentrate on Offline RL techniques. For this, we are currently using the RL-Coach library by Intel, which offers support for Batch/Offline RL. More specifically, to evaluate policies in offline settings, we train a DDQN-BCQ model and evaluate the learned policies using Offline …
As far as I know when it comes to theory, we use Pearson correlation when we want to check the correlation between two variables, which are both continuous or discrete. For a mixed case it's not so easy to use it to compute correlation coefficient. On the other hand, we have Pearson correlation estimators, where we can calculate mixed case without any problems (based on samples). Does the Pearson correlation coefficient give deceptive results in this case ?
For example, if I want to know a page views/relative prevalence of a Reddit post, and I have the upvote and downvote data. Is it valid that I use the upvote and downvote to predict that, even if I will never get the page views of that post?
In data assimilation, one assumes the existence of a observation operator $\mathcal{H}$ that maps the model-state vector $\bf{x_b}$ to $ \bf{y_b}$ (the model-equivalent of the observations $\bf{y_o}$) according to a reference I'm using to develop a preliminary understanding of DA. Can someone please elaborate on the precise meaning of: model-equivalent of the observations $\bf{y_o}$ and the methods one can use to estimate the operator $\mathcal{H}$.
Inertial measurement units (IMU), usually composed of accelerometers and gyroscopes; are well known to have inherent errors in their data, originating from bias, random walk noise, temperature dependence etc. creating a highly non-linear dependence. Typically, extended Kalman filters are used to estimate and remove these errors for stable measurement of orientations and angular velocities: but even this is not entirely accurate, as some higher order errors are ignored or approximated, and the fact that the Markov assumption ignores the effect …
In Tensorflow, there are 9 different feature columns, arranged into three groups: categorical, dense and hybrid. From reading the guide, I understand categorical columns are used to represent discrete input data with a numerical value. It gives the example of a categorical column called categorical identity column: ID Represented using one-hot encoding 0 [1, 0, 0, 0] 1 [0, 1, 0, 0] 2 [0, 0, 1, 0] 3 [0, 0, 0, 1] But you also have a dense column called …
How can i Save the TensorFlow model using estimator.export_savedmode() ? Especially, what should i put inside the serving_input_receiver_fn()? I have created a Custom Estimator based on VGGNet Architecture, i am using my own images and doing some transformation (you can see them in _parse_function()) on the images. I have read the documentation here, but i am exactly not sure what to write for my code (please see below). Ultimately i want to save the model and use TensorFlow Serving. from …
I've this code in order to visualize the most important feature of each model: dtc = DecisionTreeClassifier(min_samples_split=7, random_state=111) rfc = RandomForestClassifier(n_estimators=31, random_state=111) trained_model = dtc.fit(features_train, labels_train) trained_model.fit(features_train, labels_train) predictions = trained_model.predict(features_test) importances = trained_model.feature_importances_ std = np.std([trained_model.feature_importances_ for trained_model in trained_model.estimators_], axis=0) indices = np.argsort(importances)[::-1] for f in range(features_train.shape[1]): print("%d. feature %d (%f)" % (f + 1, indices[f], importances[indices[f]])) plt.figure() plt.title("Feature importances") plt.bar(range(features_train.shape[1]), importances[indices], color="r", yerr=std[indices], align="center") plt.xticks(range(features_train.shape[1]), indices) plt.xlim([-1, features_train.shape[1]]) plt.show() Using RandomForestClassifier this code runs good but when …
I want to plot the following estimate of the tail dependence coefficient: $\hat{\lambda}_n=\frac{1}{k}\sum_{j=1}^nI_{\{X_j>X_{(n-k)},Y_j>X_{(n-k)}\}}$ where $I_{(.)}$ is an indicator function and $X_{(1)}>...>X_{(n)}$ are order statistics. If I consider this example n=1000; alpha=4; U=runif(n); phi=0.8; sigma=0.1; X=(1-U)^{(-1/alpha)} ; Z=rnorm(n) ; Y=phi*X+sigma*abs(Z) ; then $\lambda=(.8)^4=04.09$. When I plot $\hat{\lambda}_n$ vs $k$ then the graph seems to stabilize around $0.50$ which is not true. See below the graph. n=length(X); lambda_hat=c(); lambda_hat=sapply(1:(n-1), FUN = function(i,minXY=pmin(X,Y),Xsort=sort(X)) length(minXY[minXY>Xsort[floor(n-i)]])/i); k=1:(n-1) plot(k,lambda_hat,type = "l",lwd=2,col="blue", main="Tdc of X and Y",ylab="Estimates",xlab="Order …
With a modern IMU with 9 angles of freedom collecting accelerometer, magnetometer and gyroscope data on 3 axis, what would be the best approach on filtering the data and handling it to accurately estimate the forward velocity of the swimmer? My approach was to: 1. Use a 3-point moving average to get rid of any vibrations caused by unneeded movements 2. Use a median average to get rid of repetitve movements such as shakes or water resistance 3. Perform integration …
Suppose I have a sample {$z_i$}$_{i\in[0,N]}$ = {($x_i,y_i$)}$_{i\in[0,N]}$ which commes from a probability distribution $p_z(z)$. How can I use it to estimate the mutual information between X and Y ? $MI(X,Y) = \int_Y \int_X p_z(x,y) \log{ \left(\frac{p_z(x,y)}{p_x(x)\,p_y(y)} \right) }$ where $p_x$ and $p_y$ are the marginal distributions of X and Y: $p_x(x) = \int_Yp_z(x,y)$ $p_y(y) = \int_Xp_z(x,y)$.