Deepseek

[Tom D]

They already ahead in Green technology.

Have you ever been to china to see the yellow haze hanging over most cities. I was in China long ago, couldn't miss it.

 

[Bobby Bucks]

They already ahead in Green technology.
Is it a coincidence, the app was release right after Trump became President?

Very true, the air in China is much cleaner than in the US. They wear masks in the big cities because they adhere to COVID protocols.

 

[Fernando]

Downloaded DeepSeek today. It's great providing the info I wanted.
It's a game changer for the US and the world.

 

[RCA]

It's Chinese, but it is open source and you can install it on your computer. Seems pretty safe. Word is the other AI companies will look at the code and copy their strategies.

This is a good case for competition. Nobody likes ChatGPT Pro's $200/month - unless they are filthy rich.

 

[RCA]

Apparently the code was written by recent college grads only 1-2 years out of college. Too much is made of experience. That's the thing about studying engineering - you can jump right into a good paying job after graduating from college, - well if you have the smarts.

 

[RCA]

Ok, So I finally was able to download Deepseek. Actually you install ollama and then it can download and run one of the DeepSeek models.

DeepSeek told me with my Mac Studio M2 Ultra w/64G, I could run the 32b model. It said even if I had 192G of memory on my Mac, it would not be fast enough to run a larger model. So, I have the 32b model running now. Not bad at all!

I tested it. I know the answer. It did good, -considering, but not perfect (it can't compete with somebody that really knows this stuff inside out).

MY QUESTION TO DEEPSEEEK ARE IN BOLD, OTHERWISE IT IS JUST ASKING ITSELF QUESTIONS.

>>> Can you explain how factor variables are treated in R language earth package, using multivariate adaptive regression splines?
<think>
Okay, so I'm trying to understand how the `earth` package in R handles factor variables when using Multivariate Adaptive Regression Splines
(MARS). I've heard that MARS is a flexible method for regression and classification by creating piecewise linear models. But I'm not
entirely sure about how it treats categorical variables, especially factors with multiple levels.

First, let me recall what MARS does in general. It builds a model by recursively partitioning the data space and fitting linear models
within each partition. This allows it to capture complex relationships between predictors and the response variable. The main components
are basis functions created from hinge functions like max(0, x - c) or max(0, c - x), which help in creating these partitions.

Now, considering factor variables. Factors can be binary (two levels) or have more than two levels. I think that when a factor has only two
levels, it's treated similarly to a numeric variable because it can be converted into a binary indicator (0 or 1). This makes sense because
MARS can handle binary splits effectively.

But what about factors with three or more levels? In traditional regression methods like linear models, these are typically converted into
dummy variables. For example, a factor with three levels would create two dummy variables to represent it in the model. I wonder if MARS
does something similar. Maybe each level after the first becomes an additional basis function. So for a factor with k levels, there would
be (k-1) basis functions created.

Wait, but how exactly does this work within the MARS framework? In linear models, each dummy variable is treated as a separate predictor.
Does MARS create interactions between these dummies and other variables? Or are they just included as main effects?

Also, I remember that in MARS, when you have a factor with multiple levels, it might create a set of basis functions for each level beyond
the first. So if you have a factor X with three levels (A, B, C), then two basis functions would be created: one for A vs others and
another for B vs others. This way, MARS can model how each level affects the response variable differently.

But I'm not entirely sure about the interactions. In linear models, you might have to explicitly create interaction terms between dummy
variables and other predictors if you want to include them. Does MARS automatically handle these interactions through its basis functions?
Or does it just treat each dummy as a separate main effect?

Another point is the pruning process in MARS. After creating all possible basis functions during the forward pass, the model goes through a
backward pass where it removes some terms based on their significance. I think factors with multiple levels would have their corresponding
basis functions evaluated for importance, and less important ones might be pruned out.

Let me also consider an example to solidify this understanding. Suppose we have a dataset predicting house prices with variables like
number of bedrooms (numeric) and neighborhood type (factor with three levels: Suburban, Urban, Rural). When using `earth`, the neighborhood
factor would likely create two basis functions, one for Suburban vs others and another for Urban vs others. The model would then fit linear
terms based on these categories.

During the forward pass, MARS might split the data considering both numeric variables and these new basis functions. It could find
interactions between, say, bedroom count and neighborhood type by creating product terms like max(0, bedrooms - 3) *
Suburban_basis_function. This would allow the model to capture different price effects for each neighborhood based on the number of
bedrooms.

However, I'm a bit fuzzy on whether MARS creates separate basis functions for interactions involving factors or if it treats them
differently than numeric variables. I think in `earth`, all variables are treated similarly once they're converted into appropriate
formats, so interactions can be between any two basis functions, regardless of their origin (numeric or factor).

But wait, how does this affect model interpretability? If a factor has several levels, having multiple basis functions could make the model
more complex. However, MARS uses pruning to keep only significant terms, which helps in preventing overfitting and maintaining model
simplicity.

I also remember reading that sometimes people convert factors into dummy variables before feeding them into `earth`. But according to some
sources, it's better to let `earth` handle factor variables automatically because it can manage the basis functions more efficiently,
especially when interacting with other variables. This might lead to a more accurate and parsimonious model.

In summary, my understanding is that:

1. Binary factors are treated as binary indicators (0 or 1).
2. Multi-level factors create multiple dummy basis functions.
3. These dummies can interact with other variables through product terms in the basis functions.
4. The pruning process helps in selecting only important interactions and main effects.

But I should verify if this is accurate, especially regarding how MARS specifically handles these factor-based basis functions compared to
numeric ones. Maybe looking into some examples or documentation could help clarify any uncertainties.

I think another point is that when using factors with many levels, the number of possible basis functions increases, which could
potentially lead to a more complex model. However, since `earth` includes a pruning step, it should handle this complexity by removing
unnecessary terms, keeping the model from becoming too intricate.

Also, I wonder if there's any difference in how MARS handles ordered vs unordered factors. Since factors in R can be ordered or not, but I
don't think that affects how they're treated in `earth` because it converts them into dummy variables regardless of order. The model treats
each level as a separate category without considering any inherent ordering unless specified.

Wait, actually, if the factor is ordered, maybe MARS could handle it differently by using some form of monotonicity or incorporating the
order into basis functions. But I'm not sure about that; perhaps it's better to treat ordered factors as numeric variables instead if they
have a natural order that should be respected in modeling.

Overall, my takeaway is that `earth` package in R converts factor variables into dummy variables (for multi-level) or binary indicators
(for two levels). These are then treated similarly to other predictors when building the MARS model, allowing for interactions and main
effects. The pruning process ensures that only significant terms remain, making the model both accurate and interpretable.
</think>

The `earth` package in R handles factor variables by converting them into dummy variables, which are then integrated into the Multivariate
Adaptive Regression Splines (MARS) framework. Here's a structured explanation of how this works:

1. **Binary Factors**:
- Binary factors with two levels are converted into binary indicators (0 or 1). These are treated similarly to numeric variables in
MARS.

2. **Multi-Level Factors**:
- For multi-level factors, the package creates dummy variables for each level beyond the first. For example, a factor with three levels
(A, B, C) will generate two dummy variables: one for A vs others and another for B vs others.

3. **Basis Functions**:
- These dummy variables become part of the basis functions in the MARS model. They are treated similarly to numeric predictors, allowing
interactions between dummies and other variables through product terms.

4. **Interactions**:
- The model can create interactions involving these dummy variables and other predictors, enhancing flexibility. For instance, an
interaction term might capture different effects of a factor level combined with another variable.

5. **Pruning Process**:
- During the backward pass (pruning), MARS evaluates the significance of each basis function. Less important terms, including those from
factors, may be removed to prevent overfitting and maintain model simplicity.

6. **Interpretability**:
- While multi-level factors can increase complexity, pruning helps keep the model interpretable by retaining only significant terms.

7. **Ordered vs Unordered Factors**:
- The package treats ordered and unordered factors similarly, converting them into dummy variables without considering inherent order
unless specified as numeric if an order should be respected.

In summary, `earth` efficiently handles factor variables by converting them into appropriate basis functions, allowing for flexible
modeling through interactions and main effects while maintaining model parsimony via pruning.

.... more

 

[RCA]

>>> So, there could be two factor variables and one non-factor variable in a 3rd degree interaction.
<think>
Okay, so I'm trying to understand how the `earth` package in R handles factor variables when using Multivariate Adaptive Regression Splines
(MARS). From what I gathered earlier, MARS is a flexible method that can model complex relationships by creating piecewise linear models
through basis functions, which are often built from hinge functions like max(0, x - c) or max(0, c - x).

Now, the question at hand is about how factor variables are treated in this context. Factor variables, especially those with multiple
levels, can complicate things because they're not continuous like numeric variables. I know that in traditional regression models,
categorical variables (like factors) are often converted into dummy variables to be included in the model.

So, for a binary factor (two levels), it's straightforward—it can be treated as a binary indicator (0 or 1). But what happens when there
are more than two levels? I think the `earth` package must handle this by creating multiple dummy variables for each level beyond the
first. For example, if you have a factor with three levels—A, B, and C—the package might create two dummy variables: one for A vs others
and another for B vs others.

But how does this integration happen within the MARS framework? Since MARS builds basis functions that can include interactions between
variables, these dummy variables would interact with both other factor variables and numeric variables. So, if you have two factor
variables and one non-factor variable, they could potentially form a third-degree interaction in the model.

I'm also curious about how pruning works in this context. After building all possible basis functions up to a certain degree, MARS prunes
away the less important ones to avoid overfitting. This pruning process should take into account interactions involving factor variables as
well, ensuring that only significant terms remain.

Another thing I'm thinking about is whether there's any difference between how ordered and unordered factors are handled. Ordered factors
have an inherent order to their levels, whereas unordered factors don't. Does this affect how `earth` creates the dummy variables or
interacts them within the model? Or does it treat all factor variables the same way regardless of being ordered or unordered?

I also wonder about the practical implications of having multiple factor variables in a high-degree interaction. While MARS is designed to
handle complex interactions, there must be some considerations regarding model interpretability and computational efficiency when dealing
with many levels or higher-degree interactions involving factors.

Overall, I think the key takeaway is that `earth` seamlessly integrates factor variables by converting them into dummy variables and
allowing these dummies to interact with both other factors and numeric variables within the MARS framework. The pruning process ensures
that only meaningful interactions are retained, balancing model flexibility with interpretability.
</think>

In summary, the `earth` package in R handles factor variables by converting them into dummy variables, which can then participate in
complex interactions within the Multivariate Adaptive Regression Splines (MARS) framework. Here's a structured explanation:

1. **Binary Factors**:
- Binary factors (two levels) are straightforwardly converted into binary indicators (0 or 1).

2. **Multi-Level Factors**:
- For factors with more than two levels, `earth` creates multiple dummy variables. For example, a factor with three levels (A, B, C)
would generate two dummy variables: one for A vs others and another for B vs others.

3. **Integration into MARS Framework**:
- These dummy variables are integrated into the MARS model, allowing them to interact with other factors and numeric variables. This
enables the modeling of complex relationships through higher-degree interactions.

4. **Pruning Process**:
- After constructing all potential basis functions up to a specified degree, `earth` prunes away less important terms to prevent
overfitting. This process considers interactions involving factor variables, ensuring only significant terms remain.

5. **Ordered vs. Unordered Factors**:
- There is no inherent difference in how ordered and unordered factors are handled by `earth`. Both types are converted into dummy
variables without considering their order unless explicitly specified as numeric.

6. **Considerations for High-Degree Interactions**:
- While MARS can handle high-degree interactions involving multiple factor variables, there are practical considerations regarding model
interpretability and computational efficiency.

In conclusion, `earth` effectively incorporates factor variables by converting them into dummy variables, allowing them to participate in
complex interactions within the MARS framework. The pruning process ensures that only meaningful terms are retained, balancing flexibility
with interpretability.

>>> Yes, MARS converts a factor variable with multiple values into the same number of dummy variables by concatenating the value to the end of th
... e original name. And these new dummy variables are all boolean values. But, here is the problem: The MARS model is a set of terms, each ter
... m has 1-3 variable if you are doing degree=3 type regression. You want to graph each term. How do you graph these terms if they have 0, 1,
... 2 or 3 factor variables?
<think>
Alright, I need to tackle this problem about how to graph MARS terms that involve factor variables. So, from what I understand, when using
the `earth` package in R for Multivariate Adaptive Regression Splines (MARS), factor variables with multiple levels are converted into
dummy variables. Each level of the factor becomes a new binary variable, essentially turning it into a yes/no indicator.

Okay, let's break this down step by step:

1. **Understanding MARS and Factor Variables**:
- MARS creates basis functions using hinge functions like `max(0, x - c)`. These help in creating piecewise linear models.
- For factor variables, each level beyond the first is converted into a dummy variable. So, if I have a factor with three levels (say A,
B, C), it gets split into two dummy variables: one for A vs others and another for B vs others.

2. **The Problem at Hand**:
- The user wants to graph MARS terms, especially those that involve 0, 1, 2, or 3 factor variables.
- Each term in a degree=3 model can have up to three variables, which could include both numeric and dummy variables derived from
factors.

... more ...

 

[RCA]

3. **Challenges with Graphing Terms Involving Dummy Variables**:
- If a term includes dummy variables (from factor levels), it's not straightforward to visualize because these are binary.
- For example, if a term is `dummy1 * x`, where `x` is a numeric variable and `dummy1` is a factor level indicator, how do I plot this?
- Similarly, terms with two or three dummy variables would be even more challenging.

4. **Possible Approaches**:
- Maybe there's a way to handle each combination of dummy variables separately.
- For instance, for a term involving one dummy variable, consider the cases where the dummy is 0 and where it's 1.
- When there are multiple dummies in a term, I might need to look at all possible combinations of their levels.

5. **Graphical Representation**:
- For terms with no factor variables, it's straightforward—just plot against the numeric variable(s).
- With one dummy variable, perhaps split the plot into two parts based on the dummy’s level.
- For multiple dummies, maybe use different colors or facets to represent each combination.

6. **Practical Steps**:
- Extract the terms from the MARS model and identify which involve factor variables.
- Determine how many dummy variables are part of each term.
- Based on the number of dummies, decide on an appropriate visualization strategy (split plots, color coding, etc.).

7. **Potential Pitfalls**:
- Overcomplicating the graph with too many combinations might make it hard to interpret.
- Ensuring that all possible interactions are clearly represented without clutter is crucial.

8. **Seeking Tools or Functions**:
- Are there existing R functions or packages that handle plotting MARS terms, especially those involving factor variables?
- Maybe `plotmo` package can help with visualizing the model’s predictions across different variable values.

9. **Example Scenario**:
- Suppose I have a term like `dummy1 * x + dummy2 * y`.
- How would I visualize this? Perhaps plot in 3D or use small multiples for each combination of `dummy1` and `dummy2`.

10. **Conclusion**:
- Graphing MARS terms with factor variables requires careful handling of the dummy variable combinations.
- A systematic approach, possibly involving splitting plots based on dummy levels or using advanced visualization techniques, could
address this challenge.

After considering all these points, I think the next step is to try implementing some of these ideas in R. Maybe start with a simple
example that includes a few factor levels and see how to plot the corresponding terms. It might also be helpful to look up documentation or
examples where others have dealt with similar issues.
</think>

.... more ....

 

[RCA]

To graph MARS terms involving factor variables, follow this organized approach:

1. **Extract Terms Involving Factor Variables**:
- Identify which terms in your MARS model include dummy variables derived from factor levels.

2. **Determine the Number of Dummy Variables per Term**:
- For each term, note how many dummy variables are present (e.g., 0, 1, 2, or 3).

3. **Choose a Visualization Strategy Based on Dummy Count**:
- **No Dummies**: Plot against the numeric variable(s) as usual.
- **One Dummy**: Split the plot into two parts based on the dummy's levels (e.g., using different colors or panels).
- **Two Dummies**: Use multiple facets or color coding to represent all combinations of the two dummies.
- **Three Dummies**: Consider 3D plots or small multiples for each combination.

4. **Implement Visualization in R**:
- Utilize packages like `ggplot2` for creating detailed and layered visualizations.
- Use `plotmo` package functions to assist with plotting model predictions across different variable values.

5. **Example Implementation**:
- For a term like `dummy1 * x + dummy2 * y`, consider plotting in 3D or using small multiples to represent each combination of `dummy1`
and `dummy2`.

6. **Evaluate and Refine Visualizations**:
- Ensure clarity and avoid clutter by carefully selecting how combinations are represented.
- Test different visualization techniques to find the most effective way to communicate the model's behavior.

By systematically addressing each aspect, you can effectively graph MARS terms involving factor variables, ensuring that all interactions
are clearly and interpretably visualized.

 

[Vermonter]

The inner monologue is my favorite part of Deepseek. You don't get that with the LLMs