Embed video about reinforcement learning

docs/notes/predictive-modeling/autoregressive-models/arima.qmd

@@ -1,4 +1,4 @@
-# Autocorrelation and Auto-Regressive Models
+# Auto-Regressive Models
 
 ```{python}
 #| echo: false
@@ -15,8 +15,6 @@ set_option('display.max_rows', 6)
 
 **Auto-Regressive Integrated Moving Average (ARIMA)** is a "method for forecasting or predicting future outcomes based on a historical time series. It is based on the statistical concept of serial correlation, where past data points influence future data points." - [Source: Investopedia](https://www.investopedia.com/terms/a/autoregressive-integrated-moving-average-arima.asp)
 
-In practice, ARIMA models may be better at short term forecasting, and may not perform as well in forecasting over the long term.
-
 An ARIMA model has three key components:
 
   + **Auto-Regressive (AR)** part: involves regressing the current value of the series against its past values (lags). The idea is that past observations have an influence on the current value.
@@ -26,6 +24,8 @@ An ARIMA model has three key components:
   + **Moving Average (MA)** part: involves modeling the relationship between the current value of the series and past forecast errors (residuals). The model adjusts the forecast based on the error terms from previous periods.
 
 
+In practice, ARIMA models may be better at short term forecasting, and may not perform as well in forecasting over the long term.
+
 ## Assumption of Stationarity
 
 :::{.callout-warning title="Assumption of stationarity"}
@@ -35,7 +35,7 @@ For instance, while stock *prices* are generally non-stationary, ARIMA models ca
 :::
 
 
-## Examples of ARMA Models
+## Examples
 
 :::{.callout-note title="Data Source"}
 These examples of autoregressive models are based on material by Prof. Ram Yamarthy.
@@ -65,7 +65,7 @@ df
 ```
 
 
-## Data Exploration
+#### Data Exploration
 
 Sorting data:
 
@@ -100,7 +100,7 @@ px.line(x=y.index, y=y, height=450,
 
 
 
-### Stationarity
+##### Stationarity
 
 Check for stationarity:
 
@@ -115,7 +115,7 @@ print(f'P-value: {result[1]}')
 # If p-value > 0.05, the series is not stationary, and differencing is required
 ```
 
-### Autocorrelation
+##### Autocorrelation
 
 
 Examining autocorrelation over ten lagging periods:
@@ -142,7 +142,7 @@ fig.show()
 
 We see moderately high autocorrelation persists until two to four lagging periods.
 
-## Train/Test Split
+#### Train/Test Split
 
 ```{python}
 #test_size = 0.2
@@ -169,7 +169,7 @@ print("Y TEST:", y_test.shape)
 ```
 
 
-## Model Training
+#### Model Training
 
 To implement autoregressive moving average model in Python, we can use the [`ARIMA` class](https://www.statsmodels.org/dev/generated/statsmodels.tsa.arima.model.ARIMA.html) from `statsmodels`.
 
@@ -214,7 +214,7 @@ px.line(train_set, y=["W-L%", "Predicted"], height=350,
 ```
 
 
-## Evaluation
+#### Evaluation
 
 Reconstructing test set with predictions for the test period:
 
@@ -276,3 +276,5 @@ Experimenting with different `order` parameter values may yield different result
 
 
 ### Example 2 - GDP Growth
+
+TBA

docs/notes/predictive-modeling/ml-foundations/index.qmd

@@ -63,6 +63,9 @@ Example unsupervised learning tasks include:
 **Reinforcement learning** is a different type of machine learning approach, where an "agent" learns to make decisions by interacting with an environment. The agent takes actions and receives feedback in the form of rewards or penalties, adjusting its strategy to maximize the cumulative reward over time.
 
 
+{{< video https://www.youtube.com/watch?v=kopoLzvh5jY >}}
+
+
 ## Machine Learning Problem Formulation
 
 Machine learning problem formulation refers to the process of clearly defining the task that a machine learning model is meant to solve. This step is crucial in guiding the development of the model and ensuring that the right data, techniques, and metrics are applied to achieve the desired outcome. Problem formulation involves several key components:

docs/notes/predictive-modeling/regression/index.qmd

@@ -53,7 +53,7 @@ $$
 
 Where:
 
-  + $\beta_0$ is the intercept (the value of $y$ when $X=0$
+  + $\beta_0$ is the intercept (the value of $y$ when $X=0$)
   + $\beta_1$ is the coefficient representing the slope of the line, which measures how much $y$ changes for a one-unit change in $X$
 
 

docs/notes/predictive-modeling/time-series-forecasting/seasonality.qmd

@@ -261,7 +261,7 @@ px.line(df, y=["employment", "prediction"], height=350,
 
 **Regression Residuals**
 
-Plotting residuals:
+Removing the trend, plotting just the residuals:
 
 
 ```{python}
@@ -270,6 +270,8 @@ px.line(df, y="residual",
 )
 ```
 
+There seem to be some periodic movements in the residuals.
+
 #### Seasonality via Means of Periodic Residuals
 
 Observe there may be some cyclical patterns in the residuals, by calculating periodic means:
@@ -282,7 +284,6 @@ set_option('display.max_rows', 15)
 ```
 
 ```{python}
-df = df.copy()
 df["year"] = df.index.year
 df["quarter"] = df.index.quarter
 df["month"] = df.index.month
@@ -348,18 +349,17 @@ df["prediction_monthly"] = results_monthly.fittedvalues
 df["residual_monthly"] = results_monthly.resid
 ```
 
-```{python}
-#height = 450
+Decomposition of the original data into trend, seasonal component, and residuals:
 
-#px.line(df, y=["employment", "prediction"], title="Employment vs trend", height=height)
+```{python}
+px.line(df, y=["employment", "prediction"], title="Employment vs trend", height=350)
 ```
 
 
 ```{python}
-#px.line(df, y="prediction_monthly", title="Employment vs seasonal trend", height=height)
+px.line(df, y="prediction_monthly", title="Employment seasonal component", height=350)
 ```
 
-
 ```{python}
-px.line(df, y="residual_monthly", title="Employment seasonal trend residual", height=450)
+px.line(df, y="residual_monthly", title="Employment de-trended residual", height=350)
 ```