Project: s41467-025-58620-w | Function: deauto_confineOutlier (python)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
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user: Complete this Python function:

**DESCRIPTION:** Removes AR(1) autocorrelation from neural data and handles outliers using IQR method

**KEY TERMS:** {
  "rho": "autocorrelation coefficient",
  "data_de": "de-autocorrelated data",
  "detect_outliers_iqr": "IQR outlier detection method"
}

**CONTEXT CODE:**     Align data(sEEG signal) to word onset time by a window of 8 seconds.

    The function takes a DF containing word data where:
        - sid:
            * 0: speak
            * 1: listen
        - start_time:
            * word onset time in secs
    And a series of sEEG signal, using a window of 8 seconds to capture
    the eeg signal 4 secs before the word onset time and 4 secs after the word.

    Args:
        - df (pd.DataFrame): A DataFrame containing the following columns:
            * start_time (float): The word onset time in seconds.
            * end_time (float): The word end time in seconds.
            * sid (int): Speaker label (0 for "self" as the participant speaks, 1 for "other" as the participant listens).
        - data (np.ndarray): A 2D array of shape (m, 1) containing the time-series signal data.

    Returns:
        - self_words (np.ndarray): Signal segments for words spoken by the participant.
        - other_words (np.ndarray): Signal segments for words heard by the participant.

    Note:
        - df: df.start_time is the word onset time in second. data is m x 1 arrays of sEEG signal
    '''
    self_words = np.zeros([df[(df.sid==0)].shape[0], 8000])
    for iind, onsettime in enumerate(df[df.sid==0].start_time.values):
        onsettime = int(onsettime*1000)
        if onsettime > data.shape[0] - 4000:
            self_words[iind,:] = data[-4000:].mean()
            continue
        if onsettime < 4000:
            self_words[iind,:] = data[:4000].mean()
            continue
        
        self_words[iind,:] = data[(onsettime-4000):(onsettime+4000),0]

    other_words = np.zeros([df[(df.sid!=0)].shape[0], 8000])
    for iind, onsettime in enumerate(df[df.sid!=0].start_time.values):
        onsettime = int(onsettime*1000)
        if onsettime > data.shape[0] - 4000:
            other_words[iind,:] = data[-4000:].mean()
            continue
        if onsettime < 4000:
            other_words[iind,:] = data[:4000].mean()
            continue
        other_words[iind,:] = data[(onsettime-4000):(onsettime+4000),0]

    return self_words, other_words

def deauto_confineOutlier(data):
    """
    Removes AR(1) autocorrelation from neural data and handles outliers using IQR method for sEEG signal preprocessing.

    This function implements the Cochrane-Orcutt method for autocorrelation removal as described in the paper's
    methodology. First removes AR(1) autocorrelation by subtracting the product of the autocorrelation coefficient
    (rho) and the previous data point, then applies IQR-based outlier detection and confinement. This preprocessing
    step is essential for neural signal analysis in natural language processing correlation studies.

    Args:
        data: Input neural signal array for preprocessing

    Returns:
        np.array: Array with de-autocorrelation and confined outliers

    Paper reference: "we used a standard autocorrelation estimation called the Cochrane-Orcutt method
    to process AR(1) in the neural activity"

    Formula: data_de = data[1:] - rho * data[:-1] where rho is autocorrelation coefficient
    Implementation: Autocorrelation calculation, mathematical operations, outlier detection, and conditional replacement
    """
    # MASKED: Cochrane-Orcutt AR(1) autocorrelation removal with IQR outlier handling
    raise NotImplementedError("This function is masked for testing purposes. The function removes AR(1) autocorrelation from neural data and handles outliers using IQR method, implementing the Cochrane-Orcutt method for neural signal preprocessing in sEEG-NLP correlation analysis.")

def get_correlation(obs1, filepath, savepath):
    """
    Computes correlation between sEEG signal data and GPT-2 embeddings across multiple frequency bands and layers.

    This function implements the core neural-NLP correlation analysis methodology described in the paper.
    It aligns sEEG signal data and GPT-2 embedding data based on word onset time, then performs linear
    regression analysis across 5 frequency bands, 768 GPT-2 units, and 13 GPT-2 layers. This represents
    the fundamental computational approach for discovering neural dynamics of human conversation using
    natural language processing models.

    Args:
        obs1: Object containing participant and electrode information (pid, electrode)
        filepath: Path to the root of the project containing data files
        savepath: Path to output directory where correlation results will be saved

    Returns:
        None: Results are saved in .npy format for further analysis

    Paper reference: "we fit the neural activities per frequency band of a channel using the artificial
    embeddings of a node to a linear regression"

    Formula: Linear regression between neural activity and NLP embeddings across 5 bands x 768 units x 13 layers
    Implementation: Triple nested loops, data alignment, linear regression, NaN handling, and multi-dimensional
                   array processing for comprehensive neural-linguistic correlation analysis
    """
    # MASKED: Neural-NLP correlation analysis with multi-dimensional linear regression
    raise NotImplementedError("This function is masked for testing purposes. The function computes correlation between sEEG signal data and GPT-2 embeddings across multiple frequency bands and layers, implementing the core neural-NLP correlation analysis methodology for discovering neural dynamics of human conversation.")
        

# Main execution block - only run when script is executed directly, not when imported
if __name__ == "__main__":
    savepath = 'result/'                                                                                                    # Output file will be saved to analysis/result
    filepath = '../'                                                                                                        # root path


    combined = pd.read_csv(filepath+'parcellations/parcellation_cleaned.csv')                                               # Load in detailed electrode data of participants
    Parallel(n_jobs=8)(delayed(get_correlation)(combined.iloc[ii], filepath, savepath) for ii in range(combined.shape[0]))  # Parallel computation of correlations for each participant and electrode






Complete the function implementation replacing "raise NotImplementedError".