Enforcing Valid Parameters for Negative Binomial Distributions with PyTorch

Understanding Negative Binomial Distribution

• Each Bernoulli trial has a probability of success (probs).
• Represents the number of successful trials required before a certain number of failures (total_count) occur in a series of independent Bernoulli trials.

arg_constraints Attribute

• Ensures that the distribution is well-defined and mathematically sound.
• Defines the valid range of values for the parameters of the NegativeBinomial distribution.

Constraint Details

• 'total_count'
  
  • Requires total_count to be non-negative (greater than or equal to zero).
  • This makes sense because the number of failures cannot be negative.
  • PyTorch likely uses a constraint class like constraints.GreaterEqual(lower_bound=0.0) to enforce this.

Missing Constraint for probs

• However, it's implied that probs should be within the half-open interval [0, 1).
  • Values less than 0 wouldn't represent valid probabilities (negative success probability).
  • Values exactly equal to 1 would result in a degenerate distribution where all trials succeed, which might not be desirable in all cases.

In Summary

• While not explicitly documented, probs is likely expected to be in the range [0, 1) for meaningful probability distributions.
• arg_constraints in NegativeBinomial guarantees that total_count is non-negative.

• It's generally good practice to ensure probs falls within the [0, 1) interval for standard negative binomial distributions.
• The lack of an explicit constraint for probs might be because PyTorch allows for more flexibility in distribution creation. For example, you could create a negative binomial distribution with probabilities outside the [0, 1) range for specific use cases, but these might not have well-defined properties.

---

import torch
from torch.distributions import NegativeBinomial

# Valid parameters (total_count non-negative, probs within [0, 1))
total_count = 5  # Number of failures before stopping
probs = 0.7  # Probability of success in each trial

# Create the NegativeBinomial distribution
dist = NegativeBinomial(total_count, probs)

# Sample from the distribution (number of successful trials)
samples = dist.sample((2, 3))  # Sample shape (2 batches, 3 samples each)
print(samples)

This code defines a NegativeBinomial distribution with total_count=5 (non-negative) and probs=0.7 (within the expected range). It then samples a few values from the distribution using dist.sample.

While PyTorch doesn't explicitly raise errors for probs outside the [0, 1) range, it's essential to keep these constraints in mind for mathematically sound probability distributions.

# Invalid total_count (negative)
total_count = -2
try:
  dist = NegativeBinomial(total_count, probs)
except ValueError:
  print("Error: total_count must be non-negative.")

# Invalid probs (outside [0, 1))
probs = 1.2
try:
  dist = NegativeBinomial(total_count, probs)
except ValueError:
  print("Error: probs must be between 0 and 1 (exclusive).")

This code attempts to create distributions with invalid parameters and demonstrates potential error handling (assuming probs constraint is explicitly enforced).

---

1. • You can write your own code to explicitly check if the provided parameters (total_count and probs) fall within the desired constraints before creating the distribution object.
   • This gives you granular control over the validation process.

   import torch
   from torch.distributions import NegativeBinomial
   
   def create_negative_binomial(total_count, probs):
       if total_count < 0:
           raise ValueError("total_count must be non-negative.")
       if probs < 0 or probs >= 1:
           raise ValueError("probs must be between 0 and 1 (exclusive).")
       return NegativeBinomial(total_count, probs)
   
   # Example usage
   try:
       dist = create_negative_binomial(5, 0.7)
       print("Valid distribution created.")
   except ValueError as e:
       print(f"Error: {e}")
   

2. Custom Distribution Class
   

   • You can create a custom distribution class that inherits from NegativeBinomial and overrides the __init__ method.
   • Within the __init__ method, perform the necessary checks and raise an error if the parameters violate the constraints.
   • This approach encapsulates the validation logic within your custom class.

   import torch
   from torch.distributions import NegativeBinomial
   
   class ValidatedNegativeBinomial(NegativeBinomial):
       def __init__(self, total_count, probs, validate_args=None):
           if total_count < 0:
               raise ValueError("total_count must be non-negative.")
           if probs < 0 or probs >= 1:
               raise ValueError("probs must be between 0 and 1 (exclusive).")
           super().__init__(total_count, probs, validate_args=validate_args)
   
   # Example usage
   try:
       dist = ValidatedNegativeBinomial(5, 0.7)
       print("Valid distribution created.")
   except ValueError as e:
       print(f"Error: {e}")
   

Choosing the Right Approach

• For more advanced constraint management or integration with other libraries, explore third-party options.
• If you want to encapsulate the logic within a reusable class, consider a custom distribution class.
• For simple validation needs, manual checks might suffice.