Skip to main content

Unveiling Hidden Neural Codes: SIMPL – A Scalable and Fast Approach for Optimizing Latent Variables and Tuning Curves in Neural Population Data

Dr. Rishabh Pathak
This research paper presents SIMPL (Scalable Iterative Maximization of Population-coded Latents), a novel, computationally efficient algorithm designed to refine the estimation of latent variables and tuning curves from neural population activity. Latent variables in neural data represent essential low-dimensional quantities encoding behavioral or cognitive states, which neuroscientists seek to identify to understand brain computations better. Background and Motivation Traditional approaches commonly assume the observed behavioral variable as the latent neural code. However, this assumption can lead to inaccuracies because neural activity sometimes encodes internal cognitive states differing subtly from observable behavior (e.g., anticipation, mental simulation). Existing latent variable models face challenges such as high computational cost, poor scalability to large datasets, limited expressiveness of tuning models, or difficulties interpreting complex neural network-based functio...
Post a Comment

Predicting Probabilities

Image
Dr. Rishabh Pathak

1. What is Predicting Probabilities?

  • The predict_proba method estimates the probability that a given input belongs to each class.
  • It returns values in the range [0, 1], representing the model's confidence as probabilities.
  • The sum of predicted probabilities across all classes for a sample is always 1 (i.e., they form a valid probability distribution).

2. Output Shape of predict_proba

  • For binary classification, the shape of the output is (n_samples, 2):
  • Column 0: Probability of the sample belonging to the negative class.
  • Column 1: Probability of the sample belonging to the positive class.
  • For multiclass classification, the shape is (n_samples, n_classes), with each column corresponding to the probability of the sample belonging to that class.

3. Interpretation of predict_proba Output

  • The probability reflects how confidently the model believes a data point belongs to each class.
  • For example, in binary classification:

Input Sample

Predicted Probability (Negative Class)

Predicted Probability (Positive Class)

1

0.2

0.8

2

0.9

0.1
  • The model predicts positive class if the positive class probability is greater than a threshold (default 0.5).

4. Relation to Thresholding and Classification

  • The default threshold for making classification decisions is 0.5:
  • If predict_proba for positive class > 0.5, sample is classified as positive.
  • Otherwise, it is classified as negative.
  • You can adjust this threshold depending on the problem, which affects false positive and false negative rates.
  • Adjusting thresholds can optimize metrics like precision, recall, F-score, especially on imbalanced datasets.

5. Calibration of Probability Estimates

  • Not all models produce well-calibrated probabilities.
  • A calibrated model outputs probabilities that closely match true likelihoods.
  • Example of a poor calibration: a decision tree grown to full depth might assign probability 1 or 0, but be often wrong.
  • Calibration can be improved using methods like:
  • Platt scaling
  • Isotonic regression
  • Reference: Paper by Niculescu-Mizil and Caruana, “Predicting Good Probabilities with Supervised Learning”.

6. Examples Using predict_proba (from the book)

  • Using a GradientBoostingClassifier on toy datasets:
# Suppose gbrt is a trained GradientBoostingClassifier
print("Shape of probabilities:", gbrt.predict_proba(X_test).shape)
# Output:
# Shape of probabilities: (n_samples, 2)
 
print("Predicted probabilities:\n", gbrt.predict_proba(X_test[:6]))
  • Output shows actual predicted probabilities for each class:
[[0.1 0.9]
[0.8 0.2]
[0.7 0.3]
...
]
  • The first column corresponds to the first class probability, the second column to the second class.

7. Advantages of predict_proba

  • Provides interpretable uncertainty estimates in terms of probabilities.
  • Useful for decision making where probabilistic thresholds are preferable to hard decisions.
  • Can be integrated into pipelines that weigh risks (e.g., medical diagnosis, fraud detection).
  • Helps in ranking samples by probability to prioritize further analysis.

8. Relationship Between predict_proba and decision_function

  • Some classifiers implement both decision_function and predict_proba:
  • decision_function returns raw scores or margins.
  • predict_proba converts these scores to probabilities.
  • Probabilities are usually obtained by applying a logistic function or softmax on the decision function scores.
  • Calibrated models provide better probability estimates compared to raw scores alone,.

9. Practical Considerations

  • When probabilities are needed (e.g., for risk assessment), prefer models supporting predict_proba.
  • Be cautious that probabilities are only as good as model calibration.
  • Always validate probabilities with calibration plots or metrics like Brier score.

10. Summary Table

Aspect

Details

Purpose

Provides class membership probabilities

Output Shape

Binary: (n_samples, 2), Multiclass: (n_samples, n_classes)

Values

Probabilities between 0 and 1, sum to 1 per sample

Default threshold

0.5 for binary classification

Calibration

Models may need calibration for accurate probabilities

Applications

Threshold tuning, risk assessment, ranking predictions

Relation

Derived from decision_function scores via logistic or softmax

Example Models

GradientBoostingClassifier, Logistic Regression, Random Forest

 

Categories:

Comments

Post a Comment

Popular posts from this blog

Linear Models

Dr. Rishabh Pathak
1. What are Linear Models? Linear models are a class of models that make predictions using a linear function of the input features. The prediction is computed as a weighted sum of the input features plus a bias term. They have been extensively studied over more than a century and remain widely used due to their simplicity, interpretability, and effectiveness in many scenarios. 2. Mathematical Formulation For regression , the general form of a linear model's prediction is: y^ ​ = w0 ​ x0 ​ + w1 ​ x1 ​ + … + wp ​ xp ​ + b where; y^ ​ is the predicted output, xi ​ is the i-th input feature, wi ​ is the learned weight coefficient for feature xi ​ , b is the intercept (bias term), p is the number of features. In vector form: y^ ​ = wTx + b where w = ( w0 ​ , w1 ​ , ... , wp ​ ) and x = ( x0 ​ , x1 ​ , ... , xp ​ ) . 3. Interpretation and Intuition The prediction is a linear combination of features — each feature contributes prop...
Post a Comment
Read more

Mesencephalic Locomotor Region (MLR)

Dr. Rishabh Pathak
The Mesencephalic Locomotor Region (MLR) is a region in the midbrain that plays a crucial role in the control of locomotion and rhythmic movements. Here is an overview of the MLR and its significance in neuroscience research and motor control: 1.       Location : o The MLR is located in the mesencephalon, specifically in the midbrain tegmentum, near the aqueduct of Sylvius. o   It encompasses a group of neurons that are involved in coordinating and modulating locomotor activity. 2.      Function : o   Control of Locomotion : The MLR is considered a key center for initiating and regulating locomotor movements, including walking, running, and other rhythmic activities. o Rhythmic Movements : Neurons in the MLR are involved in generating and coordinating rhythmic patterns of muscle activity essential for locomotion. o Integration of Sensory Information : The MLR receives inputs from various sensory modalities and higher brain regions t...
Post a Comment
Read more

Seizures

Dr. Rishabh Pathak
Seizures are episodes of abnormal electrical activity in the brain that can lead to a wide range of symptoms, from subtle changes in awareness to convulsions and loss of consciousness. Understanding seizures and their manifestations is crucial for accurate diagnosis and management. Here is a detailed overview of seizures: 1.       Definition : o A seizure is a transient occurrence of signs and/or symptoms due to abnormal, excessive, or synchronous neuronal activity in the brain. o Seizures can present in various forms, including focal (partial) seizures that originate in a specific area of the brain and generalized seizures that involve both hemispheres of the brain simultaneously. 2.      Classification : o Seizures are classified into different types based on their clinical presentation and EEG findings. Common seizure types include focal seizures, generalized seizures, and seizures of unknown onset. o The classification of seizures is esse...
Post a Comment
Read more

Mu Rhythms compared to Ciganek Rhythms

Dr. Rishabh Pathak
The Mu rhythm and Cigánek rhythm are two distinct EEG patterns with unique characteristics that can be compared based on various features.  1.      Location : o     Mu Rhythm : § The Mu rhythm is maximal at the C3 or C4 electrode, with occasional involvement of the Cz electrode. § It is predominantly observed in the central and precentral regions of the brain. o     Cigánek Rhythm : § The Cigánek rhythm is typically located in the central parasagittal region of the brain. § It is more symmetrically distributed compared to the Mu rhythm. 2.    Frequency : o     Mu Rhythm : §   The Mu rhythm typically exhibits a frequency similar to the alpha rhythm, around 10 Hz. §   Frequencies within the range of 7 to 11 Hz are considered normal for the Mu rhythm. o     Cigánek Rhythm : §   The Cigánek rhythm is slower than the Mu rhythm and is typically outside the alpha frequency range. 3. ...
Post a Comment
Read more

Relation of Model Complexity to Dataset Size

Dr. Rishabh Pathak
Core Concept The relationship between model complexity and dataset size is fundamental in supervised learning, affecting how well a model can learn and generalize. Model complexity refers to the capacity or flexibility of the model to fit a wide variety of functions. Dataset size refers to the number and diversity of training samples available for learning. Key Points 1. Larger Datasets Allow for More Complex Models When your dataset contains more varied data points , you can afford to use more complex models without overfitting. More data points mean more information and variety, enabling the model to learn detailed patterns without fitting noise. Quote from the book: "Relation of Model Complexity to Dataset Size. It’s important to note that model complexity is intimately tied to the variation of inputs contained in your training dataset: the larger variety of data points your dataset contains, the more complex a model you can use without overfitting....
Post a Comment
Read more