You are reading the article How To Interpret Hidden State In Latent Markov Model updated in December 2023 on the website Minhminhbmm.com. We hope that the information we have shared is helpful to you. If you find the content interesting and meaningful, please share it with your friends and continue to follow and support us for the latest updates. Suggested January 2024 How To Interpret Hidden State In Latent Markov Model
In some of my previous articles, I have illustrated how Markov model can be used in real life forecasting problems. As described in these articles, Simple Markov model cannot be used for customer level predictions, because it does not take into account any covariates for predictions. Latent Markov model is a modified version of the same Markov chain formulation, which can be leveraged for customer level predictions. “Latent” in this name is a representation of “Hidden states”. In this article, our focus will not be on how to formulate a Latent Markov model but simply on what do these hidden state actually mean. This is a concept which I have found quite ambiguous in the web world and too much statistics to understand this simple concept. In this article, I will try to illustrate physical interpretation of this concept “Hidden state” using a simple example.
[stextbox id=”section”] Case Background [/stextbox]
A prisoner was trying to escape from the prison. He was told that he will be sent a help from outside the prison, the first day when it rains. But, he was caught having a fight with his cellmate and sentenced for stay in a dark cell for a day. He is good with probabilities and will like to make inference about the weather outside. In case he gets a probability more than 50% of the day being rainy, he will make a move else will not attract attention unnecessarily. The only clue he gets in the dark cell is the accessories, which the policeman carries while coming to the cell. Given that the policeman carries Food plate wrapped in polythene 25% of times, Food plate in packed container 25% times and open food plate 50% of times; what is the probability that it will rain the same day when the prisoner is in the dark cell?
[stextbox id=”section”] Using case to build analogies [/stextbox]
In this case we have two key events. First event is “what accessories does the policeman carry” and second event is that “it will rain on the day when the prisoner is in the dark cell”.
[stextbox id=”grey”]
What accessories does the policeman carry : Observation or Ownership
it will rain on the day when the prisoner is in the dark cell : Hidden state
[/stextbox]
Hidden state and Ownership are commonly used terms in LMM model. As you can see that the observation is something the prisoner can see and accurately determine at any point of time. But the event of raining the day when he is in dark cell is something which he can only infer and not state with 100% accuracy.
[stextbox id=”section”] Calculations [/stextbox]
Having understood the concept of hidden states, let’s crunch some numbers to come up with the final probability of it raining on the day prisoner is in the dark cell. Prisoner being anxious for last few days about the weather was noting the weather for last few months. Based on these sequence, he has make a Markov chain for the weather next day given the weather of that day. Following is how the chain looks like :
The prisoner knows that it didn’t rain yesterday (Obviously, otherwise he would not have been in jail anymore). If he uses the Markov chain directly, he can conclude with some accuracy whether it will rain today or not. Following is the formulation for such a calculation :
[stextbox id=”grey”]
P(Rain today/No Rain yesterday)= 5%
[/stextbox]
Hence, the chances seem really low that it is raining out today. Now, let’s bring in some amount of information on the observation or ownership. Using some good judgement, the prisoner already knows the following conditional probability Matrix :
Let’s take one cell to clarify the grid. The chances are 90% that it is raining today if we already know that the policeman is carrying the food plate with a polythene without taking into account the weather of last day. The prisoner is keenly waiting for the policeman to come and give the final clue to determine the final set of probability. The policeman actually brings in food with a polythene. Before making calculations, let’s first decide the set of events.
[stextbox id=”grey”]
A : It will rain today
B: It did not rain yesterday
C: The policeman brings in food with a polythene
[/stextbox]
What we want to calculate is P(A/B,C)? Now let’s look at the set of probabilities we know :
[stextbox id=”grey”]
P(A/B) = 5% P(C/A) = 90% P(C) = 25%
[/stextbox]
We now will convert the expression P(A/B,C) into these know 3 parameters.
[stextbox id=”grey”]
P(A/B,C) = P(A,B/C)/P(B/C) = P(A,B/C)/P(B) {Using Markov first order principle} …………………………1
P(A,B/C) = P(A,B,C)/P(C) = P(C/A,B)*P(A,B)/P(C) = P(C/A)*P(A,B)/P(C) {Using Markov first order principle}
Substituting this in equation 1,
P(A/B,C) = P(C/A) * P(A/B) / P(C) = 90%*5%/25% = 18%
[/stextbox]
[stextbox id=”section”] Final inferences [/stextbox]
P(It will rain today/no rain yesterday,policeman brings in food with a polythene) = 18%
As you can see, this probability is between 5% and 90% as estimated separately by the two clues we have for prediction. Combination of both the clues reveals a more accurate prediction of the event in focus. Because this probability is less than 50%, the prisoner will not take a chance expecting a rain today.
[stextbox id=”section”] End Notes [/stextbox]
Using Markov chain simplifications , observations and Markov chain transition probability we were able to find out the hidden state for the day when prisoner was in the dark cell. The scope of this article was restricted to understanding hidden states and not framework of Latent Markov model. In some of the future article we will also touch up on formulation of Latent Markov model and its applications.
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How To Restart Your Iphone (Any Model)
iOS is stable, but even a stable operating system can succumb to random bugs, glitches, and other software-related snags. Like any other desktop or mobile device, restarting your iPhone is often the best way to fix a problem.
A soft reset clears the iPhone’s system cache and provides an excellent starting point to perform additional troubleshooting. Read on to learn multiple ways to restart any iOS device.
Table of Contents
Why You Should Restart Your iPhoneRebooting your iPhone can resolve numerous issues that prevent the device from functioning correctly. For example, you can give it a shot if:
Do not restart your iPhone without reason. iOS generally does a terrific job at keeping everything running in top shape, and you could go for months on end without rebooting your device.
Restart the iPhone Through the iOS Settings AppThe Settings app on your iPhone features a dedicated Shut Down option that you can use to turn off and reboot the device. It’s available on every iOS device, including the iPad.
1. Open the Settings app on your iPhone. If you can’t locate it, swipe down from the top of the Home Screen to invoke Search. Then, try searching for it.
2. Tap the category labeled General.
3. Scroll down the General screen, and tap Shut Down.
4. Tap and drag the Power icon to the right.
5. Once the iPhone’s screen goes dark, wait for at least 30 seconds.
6. Hold down the Power button. You can find it on the right side of the device (iPhone 6 and later) or at the top (iPhone 5 and earlier).
7. Release the Power button once you see the Apple logo.
8. Enter the device passcode on the Lock Screen to unlock your iPhone and restore Face ID or Touch ID.
Restart iPhone Using Device-Specific Button PressesThe method above aside, you can use the following device-specific instructions to restart your iPhone. The process varies depending on whether you use an iPhone with Face ID or Touch ID.
Restart iPhone with Face IDIf you use an iPhone with Face ID, you can press the Volume buttons and the Sleep/Wake button on the device in a specific sequence to access the Slide to Power Off screen. Then, it’s just a matter of turning the device off and booting it up again.
The steps that follow apply to the following iPhone models with Face ID:
1. Immediately press and release the Volume Up button.
2. Immediately press and release the Volume Down button.
3. Immediately press and hold the Sleep/Wake (Side) button until you see the Slide to Power Off screen.
4. Tap and drag the Power icon to the right.
5. Once the screen goes dark, wait for at least 30 seconds.
6. Hold down the Side button until you see the Apple logo.
7. Enter your device passcode to get into the Home Screen.
Tip: You can also get to the Slide to Power Off screen by pressing and holding the Volume Up and the Side buttons. Make sure to release the buttons immediately to avoid triggering an automatic call to emergency services.
Restart iPhone With Touch IDRestarting an iPhone 6 or a newer iPhone that uses Touch ID is much easier than a device with Face ID.
The steps that follow apply to the following iPhone models with a physical Home button:
1. Press and hold the Sleep/Wake (Side) button until you get to the Slide to Power Off screen.
2. Drag the Power Off slider to the right.
3. Once the iPhone’s screen goes dark, wait for at least 30 seconds.
4. Press and hold the Side button until you see the Apple logo.
5. Enter your passcode to get into the Home Screen.
Restart iPhone 5s and EarlierYou can restart an older iPhone model, such as an iPhone 5s or earlier, by following the same steps for newer devices with Touch ID. However, these devices have the Sleep/Wake button positioned at the top-right corner.
Restart iPhone Using AssistiveTouchAssistiveTouch is an accessibility-related feature that can help you restart your iPhone without you having to press any buttons whatsoever. Go through the steps below to activate and use AssistiveTouch to reboot an iOS device.
2. Turn on the switch next to AssistiveTouch.
Note: AssistiveTouch features a host of options to help you perform everyday tasks such as activating the App Switcher, taking screenshots, performing gestures, etc. You can choose to keep or disable it after restarting your iPhone.
Can’t Restart Your iPhone?How To Use Keras Model With Examples?
Introduction to Keras Model
Keras models are special neural network-oriented models that organize different layers and filter out essential information. The Keras model has two variants: Keras Sequential Model and Keras Functional API, which makes both the variants customizable and flexible according to scenario and changes. Moreover, it makes the functional APIs give a set of inputs and outputs with a single file, giving the graph model’s look and feel accordingly. It is a library with high-level language considered for deep learning on top of TensorFlow and Theano. It is written in Python language.
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What is Keras Model?Keras model is used for designing and working with neural network types that are used for building many other similar formats of architecture possessing training and feeding complex models with structures. It comprises many graphs that support the representation of a model in some other ways, with many other configurable systems and patterns for feeding values as part of training. Moreover, it provides modularity, which helps make flexible and well-suited models for customization and support. Two approaches based on this help develop sequential and functional models.
How to Use Keras model?
As the Keras model is a python-based library, it must be used for flexibility and customized model design, especially for prediction.
Keras model has its way of detecting trends with behavior for modeling and prediction.
Keras model uses a model.predict() class and reconstructed_model.predict(), which have their own significance.
Predict () class within a model can be used for creating and fitting trained data using prediction.
Another class, i.e., reconstructed_model.predict() within a model, is used to save and load the model for reconstruction. A reconstructed model compiles and retains the state into optimization using either historical or new data.
Certain components will also get incorporated or are already part of the Keras model for customization, which is as follows:
Optimizer: It is used for compiling a Keras model by passing certain arguments containing the Optimizer loss function to minimize and handle any unpredictable loss.
Loss of set and metrics: A model is compiled and is used in a way where it is used for including losses and metrics that will get taught at the time of training or modeling.
Weights: Certain input parameters must be fed to the model for required output within a Keras model.
Create Keras ModelWays to create a model using Sequential API and Functional API
1. Using Sequential APIThe idea is to create a sequential flow within layers that possess some order and help make certain flows from top to bottom, giving individual output. It helps in creating an ANN model just by calling a Sequential API() using the Keras model package, which is represented below:
model_any = sequential()
The next step is to add a layer for which a layer needs to be created, followed by passing that layer using add() function within it
model_any.add( inpt_layer)
Next, Is to access the model: which means to provide the relevant information about the layers defined or added as part of the model.
layers=model.layers
Model. input: will provide all relevant input then similarly model. the output will give relevant information about the same.
Serializing the model is another important step for serializing the model into an object like JSON and then loading it like
Then, the Summarization of the model happens, followed by Training and prediction of the model, which include components like compile, evaluate, fit, and predict.
2. Using Functional APIFunctional API is an alternative to Sequential API, where the approach is almost identical. Still, it does support and gives flexibility in terms of a certain complex model where an instance is created first, followed by connecting the layers with an input or output.
Let’s create a model by importing an input layer.
Creating an input layer where we can define dimensional input shape for a model is as follows:
data=Input(shape=(5,6)
Add a dense layer for the input
print(layer)
Define your model accordingly:
Create a model with both input and output layers using functional API:
model=Model(inpt=data, otput=layer)
Keras Model TypesKeras model represents and gels well with Deep learning; it gives the following ways to generate model types:
1. Sequential Type Model
As its name suggests, the sequential type model mostly supports and creates sequential type API, which tries to arrange the layers in a specific sequence and order.
Most deep learning and neural network have layers provisioned in a sequence for transferring data and flow from one layer to another sequence data.
2. Functional API model
This model is used to create and support some complex and flexible models.
This also helps make Directed acyclic graphs (DAGs) where the architecture comprises many layers that need to be filtered from top to bottom.
It also helps define and design branches within the architecture with some inception blocks, functions, etc.
Highlight a few famous examples supporting the Functional API model Squeeze Net, Xception, ResNet, GoogleNet, and Inception.
3. Model Subclassing
Model subclassing is a way to create a custom model comprising most of the functions and classes that are the root and internal models to the full custom forward pass model.
It does help in assisting and supporting Functional or sequential types of models for manipulation and testing.
Examples of Keras ModelBelow are the different examples of the Keras Model:
Example #1x_val_0 = x_train_0[-10020:] y_val_0 = y_train_0[-10010:] x_train_0 = x_train_0[:-10000] y_train_0 = y_train_0[:-10060] print(“prediction shape:”, prediction.shape)
Example #2This program represents the creation of a model using Sequential API ().
mode.add(Dense(16))
Example #3This program represents the creation of a model with multiple layers using functional API()
model=Model(inputsval=[input_1,input_2],outputsval=[layer_1,layer_2,layer_3])
ConclusionKeras model is used for a lot of model analysis related to deep learning and gels well with all types of the neural network, which requires an hour as most of the task carried out contains an association with AI and ANN. Tensorflow, when incorporated with Keras, makes wonder and performs quite well in analysis phases of different types of models.
Recommended ArticlesThis is a guide to Keras Model. Here we discuss the definition, how to use and create Keras Model, and examples and code implementation. You may also have a look at the following articles to learn more –
How To Find & Delete Hidden Photos With Photos Cleaner
How to Find & Delete Hidden Photos with Photos Cleaner Start Recovering The Valuable Storage Space on Android
From birthday parties to hangout sessions & private pictures, we keep them behind a security wall (hidden). & with time, maybe we forget about those or don’t bother much & feel bad about lesser storage space on the device. That’s where we need an expert solution like Photos Cleaner that helps you find the hidden files in one place & take proper action.
What Photos Cleaner is All About?If you are also looking for managing your photos perfectly & display the hidden as well open photos, go for Photos Cleaner, without a doubt. From internal as well as external media, Photos Cleaner scans for hidden pictures to help recover the storage space.
Keeping thousands of photos on your device makes your photos collection unmanageable, and duplicate photos cause additional chaos. To get rid of such images we use a duplicate cleaning tool, but what about the images that we cannot see?
You read it right, besides the photos you see in your phone’s photo Gallery there are other photos too. These usually are social media images, from the backup you have taken, etc. Finding them manually isn’t easy.
Please note: Whatever images that you deleted with Photos Cleaner, you won’t be able to recover them as they are permanently deleted.
Find & Delete Hidden Photos with Photos CleanerNow that we know how powerful & reliable Photos Cleaner software is, we should move ahead with the scanning for internal & external media. The next step would be to select the photos from the scanning result & take proper decision of deleting or keeping them. Let’s start with finding the pictures & get shocked to know that you have that many old pictures:
1. Let’s start by visiting the Play Store & downloading the Photos Cleaner tool
2. Once the downloading & installation parts have been completed, tap on Scan Photos.
3. The above command will start scanning your device for external & internal media & you will need to grant permission for that.
4. Within a few seconds, the app will display a lot of pictures along with the number of pictures.
5. Since there are many, the app will automatically divide the scanning results into different categories.
7. Now, start tapping on the ones you want to view as sometimes, you cannot view the picture properly in the grid view.
9. There are 3 ways to delete pictures, one by one, select the pictures to delete, or preview & delete if you want to.
The above process will help you take out the ‘almost trash’ files from your device that you weren’t aware of.
Don’t forget to rate the overall experience with the Photos Cleaner app by coming out to the hope page & tapping on the icon (top right corner).
Wrapping UpIntentionally or unintentionally, you had those files on your device that ultimately covered quite a good space. Now with the deletion of those files, you will be able to recover that storage space to use it for other commands.
So don’t waste much of your time & download the Photos Cleaner from Google Play Store. Install the same & let it help you reclaim the storage space back for you. & say goodbye to your old unnecessary pictures.
Next Read:
Best Android Cleaner Apps & Optimizers
How to Delete Duplicate Photos Using Duplicate Photos Fixer
Quick Reaction:About the author
Ankit Agarwal
Developing Vector Autoregressive Model In Python!
This article was published as a part of the Data Science Blogathon
Introductionmultivariate time series have more than one time-dependent variable. Each variable depends not only on its past values but also has some dependency on other variables.
Vector AutoRegressive (VAR)Vector AutoRegressive (VAR) is a multivariate forecasting algorithm that is used when two or more time series influence each other.
Let’s understand this be one example. In general univariate forecasting algorithms (AR, ARMA, ARIMA), we predict only one time-dependent variable. Here ‘Money’ is dependent on time.
Now, suppose we have one more feature that depends on time and can also influence another time-dependent variable. Let’s add another feature ‘Spending’.
Here we will predict both ‘Money’ and ‘Spending’. If we plot them, we can see both will be showing similar trends.
The main difference between other autoregressive models (AR, ARMA, and ARIMA) and the VAR model is that former models are unidirectional (predictors variable influence target variable not vice versa) but VAR is bidirectional.
A typical AR(P) model looks like this:
A K dimensional VAR model of order P, denoted as VAR(P), consider K=2, then the equation will be:
For the VAR model, we have multiple time series variables that influence each other and here, it is modelled as a system of equations with one equation per time series variable. Here k represents the count of time series variables.
In matrix form:
The equation for VAR(P) is:
VAR Model in PythonLet us look at the VAR model using the Money and Spending dataset from Kaggle. We combine these datasets into a single dataset that shows that money and spending influence each other. Final combined dataset span from January 2013 to April 2023.
Steps that we need to follow to build the VAR model are:
7. If necessary, invert the earlier transformation.
1. Examine the DataFirst import all the required libraries
import pandas as pd import numpy as np import matplotlib.pyplot as plt %matplotlib inlineNow read the dataset
money_df = pd.read_csv('M2SLMoneyStock.csv') spending_df = pd.read_csv('PCEPersonalSpending.csv') df = money_df.join(spending_df)
2. Check for StationarityBefore applying the VAR model, all the time series variables in the data should be stationary. Stationarity is a statistical property in which time series show constant mean and variance over time.
One of the common methods to perform a stationarity check is the Augmented Dickey-Fuller test.
In the ADF test, there is a null hypothesis that the time series is considered non-stationary. So, if the p-value of the test is less than the significance level then it rejects the null hypothesis and considers that the time series is stationary.
def adf_test(series,title=''): """ Pass in a time series and an optional title, returns an ADF report """ print(f'Augmented Dickey-Fuller Test: {title}') result = adfuller(series.dropna(),autolag='AIC') # .dropna() handles differenced data labels = ['ADF test statistic','p-value','# lags used','# observations'] out = pd.Series(result[0:4],index=labels) for key,val in result[4].items(): out[f'critical value ({key})']=val print(out.to_string()) # .to_string() removes the line "dtype: float64" if result[1] <= 0.05: print("Strong evidence against the null hypothesis") print("Reject the null hypothesis") print("Data has no unit root and is stationary") else: print("Weak evidence against the null hypothesis") print("Fail to reject the null hypothesis") print("Data has a unit root and is non-stationary")Check both the features whether they are stationary or not.
adf_test(df['Money']) Augmented Dickey-Fuller Test: ADF test statistic 4.239022 p-value 1.000000 # lags used 4.000000 # observations 247.000000 critical value (1%) -3.457105 critical value (5%) -2.873314 critical value (10%) -2.573044 Weak evidence against the null hypothesis Fail to reject the null hypothesis Data has a unit root and is non-stationaryNow check the variable ‘Spending’.
adf_test(df['Spending']) Augmented Dickey-Fuller Test: ADF test statistic 0.149796 p-value 0.969301 # lags used 3.000000 # observations 248.000000 critical value (1%) -3.456996 critical value (5%) -2.873266 critical value (10%) -2.573019 Weak evidence against the null hypothesis Fail to reject the null hypothesis Data has a unit root and is non-stationaryNeither variable is stationary, so we’ll take a first-order difference of the entire DataFrame and re-run the augmented Dickey-Fuller test.
df_difference = df.diff() adf_test(df_difference['Money']) Augmented Dickey-Fuller Test: ADF test statistic -7.077471e+00 p-value 4.760675e-10 # lags used 1.400000e+01 # observations 2.350000e+02 critical value (1%) -3.458487e+00 critical value (5%) -2.873919e+00 critical value (10%) -2.573367e+00 Strong evidence against the null hypothesis Reject the null hypothesis Data has no unit root and is stationary adf_test(df_difference['Spending']) Augmented Dickey-Fuller Test: ADF test statistic -8.760145e+00 p-value 2.687900e-14 # lags used 8.000000e+00 # observations 2.410000e+02 critical value (1%) -3.457779e+00 critical value (5%) -2.873609e+00 critical value (10%) -2.573202e+00 Strong evidence against the null hypothesis Reject the null hypothesis Data has no unit root and is stationary 3. Train-Test SplitWe will be using the last 1 year of data as a test set (last 12 months).
test_obs = 12 train = df_difference[:-test_obs] test = df_difference[-test_obs:] 4. Grid Search for Order P for i in [1,2,3,4,5,6,7,8,9,10]: model = VAR(train) results = model.fit(i) print('Order =', i) print('AIC: ', results.aic) print('BIC: ', results.bic) print() Order = 1 AIC: 14.178610495220896 Order = 2 AIC: 13.955189367163705 Order = 3 AIC: 13.849518291541038 Order = 4 AIC: 13.827950574458281 Order = 5 AIC: 13.78730034460964 Order = 6 AIC: 13.799076756885809 Order = 7 AIC: 13.797638727913972 Order = 8 AIC: 13.747200843672085 Order = 9 AIC: 13.768071682657098 Order = 10 AIC: 13.806012266239211As you keep on increasing the value of the P model becomes more complex. AIC penalizes the complex model.
As we can see, AIC begins to drop as we fit the more complex model but, after a certain amount of time AIC begins to increase again. It’s because AIC is punishing these models for being too complex.
VAR(5) returns the lowest score and after that again AIC starts increasing, hence we will build the VAR model of order 5.
5. Fit VAR(5) Model result = model.fit(5) result.summary() Summary of Regression Results ================================== Model: VAR Method: OLS Date: Thu, 29, Jul, 2023 Time: 15:21:45 -------------------------------------------------------------------- No. of Equations: 2.00000 BIC: 14.1131 Nobs: 233.000 HQIC: 13.9187 Log likelihood: -2245.45 FPE: 972321. AIC: 13.7873 Det(Omega_mle): 886628. -------------------------------------------------------------------- Results for equation Money ============================================================================== coefficient std. error t-stat prob ------------------------------------------------------------------------------ const 0.516683 1.782238 0.290 0.772 L1.Money -0.646232 0.068177 -9.479 0.000 L1.Spending -0.107411 0.051388 -2.090 0.037 L2.Money -0.497482 0.077749 -6.399 0.000 L2.Spending -0.192202 0.068613 -2.801 0.005 L3.Money -0.234442 0.081004 -2.894 0.004 L3.Spending -0.178099 0.074288 -2.397 0.017 L4.Money -0.295531 0.075294 -3.925 0.000 L4.Spending -0.035564 0.069664 -0.511 0.610 L5.Money -0.162399 0.066700 -2.435 0.015 L5.Spending -0.058449 0.051357 -1.138 0.255 ============================================================================== 6 Predict Test DataThe VAR .forecast() function requires that we pass in a lag order number of previous observations.
lagged_Values = train.values[-8:]pred = result.forecast(y=lagged_Values, steps=12)
idx = pd.date_range('2023-01-01', periods=12, freq='MS')
df_forecast=pd.DataFrame(data=pred, index=idx, columns=['money_2d', 'spending_2d'])
7. Invert the transformation
We have to note that the forecasted value is a second-order difference. To get it similar to original data we have to roll back each difference. This can be done by taking the most recent values of the original series’ training data and adding it to a cumulative sun of forecasted values.
df_forecast['Money1d'] = (df['Money'].iloc[-test_obs-1]-df['Money'].iloc[-test_obs-2]) + df_forecast['money2d'].cumsum() df_forecast['MoneyForecast'] = df['Money'].iloc[-test_obs-1] + df_forecast['Money1d'].cumsum() df_forecast['Spending1d'] = (df['Spending'].iloc[-test_obs-1]-df['Spending'].iloc[-test_obs-2]) + df_forecast['Spending2d'].cumsum() df_forecast['SpendingForecast'] = df['Spending'].iloc[-test_obs-1] + df_forecast['Spending1d'].cumsum() Plot the ResultNow let’s plot the predicted v/s original values of ‘Money’ and ‘Spending’ for test data.
test_original = df[-test_obs:] test_original.index = pd.to_datetime(test_original.index) test_original['Money'].plot(figsize=(12,5),legend=True) df_forecast['MoneyForecast'].plot(legend=True) test_original['Spending'].plot(figsize=(12,5),legend=True) df_forecast['SpendingForecast'].plot(legend=True)The original value and predicted values show a similar pattern for both ‘Money’ and ‘Spending’.
ConclusionIn this article, first, we gave a basic understanding of univariate and multivariate analysis followed by intuition behind the VAR model and steps required to implement the VAR model in Python.
The media shown in this article are not owned by Analytics Vidhya and are used at the Author’s discretion.
Related
Florida State Medical Boards Vote To Ban Gender
Late last week, the Florida Board of Medicine and the state Board of Osteopathic Medicine voted at a joint meeting to approve a rule banning transgender minors from receiving gender-affirming care. This impacts the use of puberty-blocking hormones and gender-affirming surgeries, which typically treat gender dysphoria in minors.
The rule was finalized on November 4 at the at the urging of Republican Governor Ron DeSantis and is set to take effect after a 21-day long public input period. The decision will not apply to transgender youth who are already receiving nonsurgical treatment. However medical professionals who violate the new rule with new patients could face severe penalties—including losing their medical license.
[Related: First-of-a-kind study shows encouraging data for trans kids who socially transition.]
The guidance of medical organizations including the American Academy of Pediatrics (AAP), the Endocrine Society, the United States Department of Health and Human Services, and the American Psychological Association the Florida Surgeon General’s view that gender affirming healthcare is medically unproven or potentially dangerous in the long term. They have all endorsed using puberty blockers and hormones for young people with gender dysphoria and multiple studies have found that these treatments can reduce emotional distress for transgender young people and even reduce the risk of suicide.
“Our research team from Harvard Medical School and the Fenway Institute published a study showing that access to puberty blockers during adolescence is associated with lower odds of transgender young adults considering suicide,” Jack Turban wrote in The New York Times in February 2023, citing a study on puberty suppression. “Despite fearmongering, these are safe medications that doctors have been using for decades for cisgender children who go through puberty too early. They also are reversible — if the medication is stopped, puberty will progress.”
The two boards did disagree on whether nonsurgical treatments for gender dysphoria may continue through Institutional Review Board-approved clinical trials. The Board of Osteopathic Medicine approved of that rule, but the state Board of Medicine rejected the proposal.
In June, Florida health officials also banned state Medicaid insurance from covering gender dysphoria treatments and issued a report that said the treatments have not been proven safe or effective. The Yale School of Medicine followed up with a comprehensive examination of the report, saying that the document is misleading and doesn’t call into question any of the scientific foundations of the standard medical care for gender dysmorphia.
Florida is not alone in attempting to use state legislatures to ban or limit gender affirming care. In 2023, Arkansas became the first state to enact a ban on gender affirming care when Republican lawmakers were able to successfully override Governor Asa Hutchinson’s veto of the legislation. This year, Republicans in Alabama approved legislation that outlaws gender-affirming medications for transgender youth. Both the Arkansas and Alabama laws have been paused amid unfolding legal battles.
[Related: How to use science to talk to kids about gender.]
In October, Oklahoma Governor Kevin Stitt, signed a bill that bars federal funds earmarked for the University of Oklahoma Medical Center from being used for gender affirming treatments for minors, while calling for the state legislature to ban some gender affirming treatments when it reconvenes in February 2023. Additionally, Tennessee has passed legislation curbing trans healthcare, but it faces legal challenges. Arizona has passed four laws regarding transgender healthcare.
While these pieces of legislation continue to be tangled up in courts, groups like the Human Rights Campaign and AAP say they will continue to fight for medical care for trans youth.
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