With four parameters I can fit an elephant, and with five I can
make him wiggle his trunk.
~ John von Neumann
No telling what you
can do with 675B parameters.
DeepSeek-R1 has been all over the tech news during the last few weeks, It
scared Wall Street and forced the
big guys to rethink strategy. DeepSeek-R1 is an open-source AI language model developed by the Chinese startup DeepSeek. There are lots of
LLMs available. The big deal with DeepSeek-R1 is that it is open source. The code and parameters are available for download. It was also developed on a shoe string budget compared to the amount spent by outfits like OpenAI for developing their LLMs.
I made a few simple tests to compare DeepSeek-R1's performance against OpenAI's o1-mini. o3-mini was not available yet when I made the tests
Change Point Detection Code Generation
I gave ChatGPT o1-mini and DeepSeek-R1 (using the
web app) the same prompt.
write python code to detect change points in a time series
Here's what ChatGPT came up with.
Change point detection involves identifying points in a time series where the statistical properties (such as mean, variance, or distribution) change. Detecting these points is crucial in various applications like finance, quality control, and environmental monitoring.
Below is a Python example using the `ruptures` library, which is a powerful tool for change point detection. This example demonstrates how to detect change points in a synthetic time series and visualize the results.
### Step 1: Install Required Libraries
First, ensure you have the necessary libraries installed. You can install them using `pip`:
```bash
pip install numpy matplotlib ruptures
```
### Step 2: Python Code for Change Point Detection
```python
import numpy as np
import matplotlib.pyplot as plt
import ruptures as rpt
# Generate synthetic data with change points
def generate_data(n_samples=500, n_bkps=3, noise=1.0, seed=42):
np.random.seed(seed)
# Generate random signal
signal = np.random.normal(loc=0, scale=1, size=n_samples)
# Define change points
bkps = sorted(np.random.choice(range(50, n_samples - 50), n_bkps, replace=False))
for bp in bkps:
signal[bp:] += np.random.normal(loc=5, scale=1, size=n_samples - bp)
return signal, bkps
# Generate data
signal, true_bkps = generate_data()
# Display the generated signal
plt.figure(figsize=(10, 6))
plt.plot(signal, label='Signal')
for bp in true_bkps:
plt.axvline(x=bp, color='red', linestyle='--', label='True Change Point' if bp == true_bkps[0] else "")
plt.title("Synthetic Time Series with Change Points")
plt.xlabel("Time")
plt.ylabel("Value")
plt.legend()
plt.show()
# Change Point Detection using Pelt search method with a linear model
model = "l2" # "l2" corresponds to the least squares model
algo = rpt.Pelt(model=model).fit(signal)
result = algo.predict(pen=10) # The penalty value controls the sensitivity
# Display the detected change points
plt.figure(figsize=(10, 6))
plt.plot(signal, label='Signal')
for cp in result:
plt.axvline(x=cp, color='green', linestyle='--', label='Detected Change Point' if cp == result[0] else "")
plt.title("Detected Change Points in the Time Series")
plt.xlabel("Time")
plt.ylabel("Value")
plt.legend()
plt.show()
# Print detected change points
print("True Change Points:", true_bkps)
print("Detected Change Points:", result)
```
### Step 3: Understanding the Code
1. **Data Generation**:
- The `generate_data` function creates a synthetic time series with a specified number of change points (`n_bkps`). It adds a shift to the mean of the signal at each change point.
- This synthetic data helps demonstrate how the change point detection works.
2. **Visualization of Synthetic Data**:
- The first plot shows the generated time series with the true change points marked by red dashed lines.
3. **Change Point Detection**:
- **Model Selection**: The `"l2"` model is used, which is suitable for detecting changes in the mean of the signal.
- **Algorithm**: The PELT (Pruned Exact Linear Time) algorithm is employed for efficient change point detection.
- **Penalty Parameter**: The `pen` parameter controls the sensitivity. A higher penalty means fewer change points are detected. You might need to adjust this value based on your specific data.
4. **Visualization of Detected Change Points**:
- The second plot displays the same time series with detected change points marked by green dashed lines.
5. **Output**:
- The true and detected change points are printed to the console for comparison.
### Step 4: Customizing for Your Data
To apply change point detection to your own time series data:
1. **Load Your Data**:
Replace the synthetic data generation with loading your data, for example, using `pandas`:
```python
import pandas as pd
# Example: Loading data from a CSV file
data = pd.read_csv('your_time_series.csv')
signal = data['value_column'].values
```
2. **Adjust the Model and Parameters**:
Depending on the nature of your data and the type of changes you expect (mean, variance, etc.), you might need to choose a different model or adjust parameters like `pen`.
```python
# Example: Using a linear model if detecting changes in slope
model = "linear"
algo = rpt.Pelt(model=model).fit(signal)
result = algo.predict(pen=10)
```
3. **Experiment with Different Algorithms**:
`ruptures` offers various algorithms and models. Explore them to find the best fit for your application:
- **Dynamic Programming (`rpt.Dynp`)**:
```python
algo = rpt.Dynp(model=model).fit(signal)
result = algo.predict(n_bkps=3) # Specify the number of change points
```
- **Binary Segmentation (`rpt.Binseg`)**:
```python
algo = rpt.Binseg(model=model).fit(signal)
result = algo.predict(n_bkps=3)
```
- **Window-based (`rpt.Window`)**:
```python
algo = rpt.Window(model=model, window=50).fit(signal)
result = algo.predict(pen=10)
```
4. **Selecting the Penalty Parameter**:
Use methods like cross-validation or information criteria (e.g., Bayesian Information Criterion) to choose an appropriate penalty.
```python
# Example: Using grid search to find the optimal penalty
penalties = np.linspace(1, 100, 100)
for pen in penalties:
result = algo.predict(pen=pen)
# Evaluate the results based on your criteria
```
### Additional Resources
- **Ruptures Documentation**: [https://centre-borelli.github.io/ruptures-docs/](https://centre-borelli.github.io/ruptures-docs/)
- **Change Point Detection Survey**: [A Comprehensive Survey on Change Point Detection](https://arxiv.org/abs/1802.05535)
By leveraging the `ruptures` library and customizing the parameters and models, you can effectively detect change points in various types of time series data.
I tried the code and at least on this simple test, it worked without modification. I liked the suggestion of other algorithms to try.
Here's the response from DeepSeek-R1.
Okay, I need to write Python code to detect change points in a time series. Let me think about the steps involved. First, what's a change point? It's a point in the time series where the statistical properties change, like mean, variance, or trend. So, the goal is to find where these changes occur.
I remember there are several libraries in Python for this. One common approach is using the ruptures library, which has methods for change point detection. Another option might be using Bayesian methods with something like Prophet, but I think ruptures is more straightforward for this task.
Alright, so the steps would be: install the necessary library, load or generate some sample data, apply the change point detection algorithm, and then output or visualize the results.
Wait, the user asked for code, so I should make sure to include all necessary parts. Let's start with installing ruptures. They might not have it installed, so I should mention that. Then, import the required modules. Let me check the documentation for ruptures to recall the syntax.
Ruptures supports different algorithms, like Pelt, BinSeg, and Dynp. Pelt is efficient for detecting multiple changes. I'll probably use that. The process involves specifying a cost function (like a change in mean) and then running the detection.
Sample data: Maybe generate a synthetic time series with some known change points. For example, create a series where the mean shifts at certain points. That way, the code can demonstrate the detection effectively.
Visualization is important, so using matplotlib to plot the original series and the detected change points would be helpful. Let's outline the code structure:
1. Install ruptures if not already installed.
2. Import numpy, matplotlib, and ruptures.
3. Generate sample data with change points.
4. Apply the change point detection algorithm.
5. Retrieve the change points indices.
6. Plot the results showing the data and vertical lines at change points.
Possible issues: The choice of the cost function and penalty parameter in ruptures. The penalty affects the number of detected changes. Maybe set a reasonable penalty value or use a default. For the example, using the 'l2' cost (for changes in mean) makes sense.
Another thing: ruptures returns the indices of the change points, which are the end of each segment. So the actual change occurs after that index. Wait, no—ruptures gives the indexes where the change occurs. Need to check. For example, if a time series has a change at index 100, then the segments are from 0 to 100, then 100 to end. So the change points list would include 100 as the first change.
Let me test a small example. Suppose data is [0]*100 + [1]*100. The change is at index 100. So the algorithm should detect 100 as a change point.
In code: using ruptures, create the algorithm instance, fit the data, then predict with a penalty. The penalty parameter 'pen' in pelt needs to be set. How to choose that? Maybe start with pen=3, and adjust based on results. Alternatively, use the 'Dynp' method which requires specifying the number of changes, but Pelt is more automatic.
Putting it all together:
Installation command: !pip install ruptures (if using Jupyter), but in code comments.
Generate sample data with numpy:
import numpy as np
np.random.seed(0)
n_points = 200
data = np.concatenate(
[np.random.normal(0, 0.5, 50),
np.random.normal(2, 0.5, 50),
np.random.normal(0, 0.5, 50),
np.random.normal(-2, 0.5, 50)]
)
This creates a series with changes at 50, 100, 150.
Then, using ruptures:
import ruptures as rpt
algo = rpt.Pelt(model="l2").fit(data)
result = algo.predict(pen=10)
print("Change points detected at indices:", result)
Wait, the 'predict' method returns the list of change points. Let me check the documentation. Yes, the change points are the indices where the changes occur. So for the sample data, the expected result would be [50, 100, 150].
Then, plotting with matplotlib:
import matplotlib.pyplot as plt
plt.figure(figsize=(10,6))
plt.plot(data)
for cp in result:
plt.axvline(x=cp, color='r', linestyle='--')
plt.title("Change Points Detected")
plt.show()
But wait, the change points are at 50, 100, 150. The data starts at 0, so those indices are correct.
But need to note that the last change point is the end of the last segment. So the code will correctly mark the transitions.
Potential adjustments: The pen parameter. If the penalty is too low, more change points are detected. If too high, fewer. The user might need to adjust this based on their data. Maybe include a comment about tuning the penalty.
Alternatively, use a different model. For example, if the variance changes, use 'normal' or 'rbf' model. But for the example, 'l2' (which is least squared deviation, suitable for changes in mean) is appropriate.
Also, handling real-world data: the code assumes the data is a 1D array. So the user should input their time series as such.
Another thing: the sample data is generated with four segments, each 50 points. So the code should detect three change points.
Testing the code with the sample data should show vertical lines at the correct positions.
So the final code would include all these steps, with comments explaining each part.
Possible edge cases: data with no change points, or very noisy data. But the example is straightforward.
I think that's a solid approach. Let me write the code step-by-step as described.
To detect change points in a time series using Python, you can use the `ruptures` library, which provides efficient methods for change point detection. Here's a step-by-step example:
### Step 1: Install the Required Library
```bash
pip install ruptures numpy matplotlib
```
### Step 2: Python Code for Change Point Detection
```python
import numpy as np
import matplotlib.pyplot as plt
import ruptures as rpt
# Generate synthetic time series with change points
np.random.seed(0) # for reproducibility
n_points = 200
# Create data with shifts in mean at 50, 100, 150
data = np.concatenate([
np.random.normal(0, 0.5, 50),
np.random.normal(2, 0.5, 50),
np.random.normal(0, 0.5, 50),
np.random.normal(-2, 0.5, 50)
])
# Detect change points using the Pelt algorithm (for changes in mean)
model = "l2" # "l2" for least squared deviation (changes in mean)
algo = rpt.Pelt(model=model).fit(data)
change_points = algo.predict(pen=10) # penalty parameter (adjust based on data)
# Remove the last index (end of the signal) if included
change_points = [cp for cp in change_points if cp < len(data)]
# Plot the results
plt.figure(figsize=(10, 6))
plt.plot(data, label='Time Series')
for cp in change_points:
plt.axvline(x=cp, color='red', linestyle='--', label='Change Point' if cp == change_points[0] else "")
plt.title("Change Points Detected in Time Series")
plt.xlabel("Time")
plt.ylabel("Value")
plt.legend()
plt.show()
print(f"Detected change points at indices: {change_points}")
```
### Explanation:
1. **Synthetic Data**: A time series with four segments (changes in mean at indices 50, 100, and 150).
2. **Algorithm**: The `Pelt` algorithm from `ruptures` detects multiple change points efficiently. The `model="l2"` assumes changes in the mean.
3. **Penalty (`pen`)**: Controls sensitivity to changes. Increase `pen` to reduce the number of detected changes.
4. **Visualization**: The detected change points are marked with red dashed lines.
### Output:
- The plot shows the time series with vertical lines at detected change points.
- The console prints the indices of detected changes (e.g., `[50, 100, 150]`).
### Adjustments for Your Data:
- **Tune `pen`**: Experiment with different penalty values.
- **Model Type**: Use `model="rbf"` for variance changes or `model="linear"` for trend changes.
- **Real Data**: Replace the synthetic `data` with your time series (1D array).
For more details, refer to the [ruptures documentation](https://centre-borelli.github.io/ruptures-docs/).
DeepSeek-R1 was a bit more verbose and didn't try to suggest alternatives. However, DeepSeek did a good job of provide a readable description of the reasoning process. The code ran without modification.
I also tried the DeepSeek-7B model running it via
ollama. This model has 7 billion parameters and will run on a laptop.
Here's the output.
<think>
Okay, so the user is asking for Python code to detect change points in a time series. Hmm, I need to
figure out what exactly they mean by that. Change point detection usually refers to identifying
points where the statistical properties of the data change abruptly.
First, I should consider different methods available for this task. There's binary segmentation,
which recursively splits the data into segments and looks for changes. Then there's the Pelt
algorithm, which is more efficient for detecting multiple changes. Also, using libraries like
ruptures could be helpful since it has various algorithms implemented.
I think the user might not be familiar with all these methods, so providing a simple example would
help them get started. Maybe start with a basic setup where they import necessary libraries and
generate some synthetic data to test on.
Next, I need to outline how each method works briefly. For instance, binary segmentation splits the
time series into two parts at each step until no more changes are found. The Pelt algorithm is great
for penalizing change points, making it suitable when you have an idea of how many changes you
expect. Using a library like ruptures makes things easier because it has built-in functions to
detect multiple change points.
I should include code examples that show how to simulate data with and without change points. Then
apply each method to detect the change points. After detecting them, plotting the results would be
helpful for visualization. That way, the user can see where the changes were identified.
Wait, I should also mention that the number of change points isn't always known in advance. The
methods will determine this based on some criteria like p-values or penalties. Including a note
about tuning parameters and testing different algorithms might help them choose the best approach
for their specific data.
Oh, right, the user didn't specify which method they prefer, so providing multiple options is good.
They can then decide which one suits their needs better. I should structure the code with comments
explaining each part so it's clear how to use it.
Finally, adding a conclusion that summarizes when to use each method would be useful for the user.
This way, they know which algorithm to apply based on their situation.
</think>
To detect change points in a time series, you can use various methods depending on the type of
changes (mean shift, variance change, etc.) and the number of expected change points. Below is an
example using Python code that demonstrates how to detect change points in a synthetic time series
with known change points.
We will use three different approaches:
1. **Binary Segmentation**
2. **Pelt Algorithm** (for multiple change points)
3. **Ruptures Library**
### Step 1: Import Necessary Libraries
```python
import numpy as np
import matplotlib.pyplot as plt
from ruptures import rpt, rptl
from pelt import Pelt
```
### Step 2: Generate Synthetic Time Series Data with Change Points
Here's an example of generating a synthetic time series with two change points:
```python
n_samples = 100
n_features = 1
# First part of the time series (mean = 5, variance = 1)
X = np.random.normal(5, 1, n_samples).reshape(-1, n_features)
# Second part of the time series (mean = 8, variance = 1.5)
Y = np.random.normal(7, 1.5, n_samples).reshape(-1, n_features)
# Third part of the time series (mean = 2, variance = 0.8)
Z = np.random.normal(4, 0.8, n_samples).reshape(-1, n_features)
# Concatenate all parts
data = np.concatenate([X, Y, Z])
```
### Step 3: Add Change Points
In this example, we have three segments with different means and variances.
### Step 4: Detect Change Points Using Binary Segmentation
Binary segmentation is a recursive algorithm that splits the data into two parts at each step until
no more changes are detected. Here's how to implement it:
```python
# Define the cost function (e.g., Normal distribution)
cost = "normal"
# Initialize the change point detection model using binary segmentation
algo = rpt.Binseg(cost=cost, min_length=10).fit(data)
# Predict the change points
change_points = algo.predict(pen=0.05)
print("Change points detected at indices:", change_points)
```
### Step 5: Detect Change Points Using Pelt Algorithm
The Pelt algorithm is efficient for detecting multiple change points, especially when you have an
idea of how many changes to expect.
```python
# Define the cost function (e.g., Normal distribution with penalty)
pen = 0.1
algo_pelt = Pelt(pen=pen).fit(data)
change_points_pelt = algo_pelt.predict()
print("Change points detected at indices:", change_points_pelt)
```
### Step 6: Detect Change Points Using Ruptures Library
The ruptures library provides a variety of algorithms for change point detection. Here's an example
using the `Binseg` model from ruptures:
```python
fromruptures import BinSeg
# Initialize the change point detection model
model = BinSeg(pen=0.05)
# Detect the change points
change_points_ruptures = model.fit_predict(data, n_bkps=2) # Assuming 2 change points
print("Change points detected at indices:", change_points_ruptures)
```
### Step 7: Visualize the Results
plt.figure(figsize=(10, 6))
# Plot the original data
plt.plot(data[:, 0], label='Original Data')
# Plot the detected change points as vertical lines
for cp in change_points:
plt.axvline(x=cp, color='red', linestyle='--', linewidth=2, alpha=0.5)
for cp_pelt in change_points_pelt:
plt.axvline(x=cp_pelt, color='green', linestyle='--', linewidth=2, alpha=0.5)
for cp_ruptures in change_points_ruptures:
plt.axvline(x=cp_ruptures, color='blue', linestyle='--', linewidth=2, alpha=0.5)
plt.legend(['Original Data', 'Change Points (Binary Seg)',
'Change Points (Pelt)', 'Change Points (Ruptures)'])
plt.xlabel('Time')
plt.ylabel('Value')
plt.title('Change Point Detection in Time Series')
plt.show()
### Conclusion
- **Binary Segmentation**: This method recursively splits the data into segments and looks for
changes within each segment. It works well when you have a good idea of where to expect changes.
- **Pelt Algorithm**: This is an optimal algorithm that uses dynamic programming with pruning
(sliding window) to detect change points efficiently, especially useful for large datasets.
- **Ruptures Library**: This library provides multiple algorithms and models for detecting change
points. It's highly flexible and allows you to specify the number of expected changes.
You can choose the method based on your specific needs, such as the size of the dataset, the
expected number of change points, and whether you have prior knowledge about where the changes might
occur.
>>>
The 7B results were less impressive. The reasoning section seemed good, but the code had numerous bugs and didn't run initially. I didn't spend much time debugging it, only enough to get it to run and do something. The code chose every 5 positions in the series as a change point.
I guess it takes more than 7 billion parameters to write good code.
