DPM

Differentiable Probabilistic Models

Table of Contents

1. Distributions
2. Transforms
3. Criterion
4. Models
5. Monte Carlo

" class="reference-link">Distributions

1. Arcsine
2. Asymmetric Laplace
3. Bernoulli
4. Beta
5. Binomial
6. Categorical
7. Cauchy
8. ChiSquare
9. Conditional Model
   • Uses a Neural Network to take inputs and create the parameters of a distribution.
   • Sampling -> takes a value, runs the network to create the distribution,
     sample from conditional distribution.
   • Log Prob -> Create distribution conditioned on X, take log_prob w.r.t. Z
10. Convolution -Sum of component distributions, only allows sampling
11. Data Distribution - Randomly sample from a given set of data.
12. Dirac Delta
13. Dirichlet
14. Exponential
15. Fisher-Snedecor (F-Distribution)
16. Gamma
17. Generator
    • Uses a latent distribution to sample inputs to a neural network to
      generate a distribution. Train with the adversarial losses.
18. Geometric
19. Gumbel Softmax (Relaxed Categorical)
20. Gumbel
21. Half Cauchy
22. Half Normal
23. Hyperbolic Secant
24. Kumaraswamy
25. Langevin
    • Adds Langevin Dynamics to sampling methods (see wikipedia)
26. Laplace
27. Log Cauchy
28. Log Laplace
29. Log Normal
30. Logistic
31. Logit Normal
32. Negative Binomial
33. Normal (Multivariate)
34. Normal (Independent)
35. Pareto
36. Poisson
37. Rayleigh
38. Relaxed Bernoulli
39. Student T
40. Transform Distribution
    • Composes a list of transforms on a distribution
    • Example: Exp(Normal) ~ LogNormal
41. Uniform)
42. Weibull
43. Mixture Model
    • Static weights to pick from sub-models using a categorical distribution.
44. Gumbel Mixture Model
    • Uses the Gumbel Softmax as a differentiable approximation to the
      categorical distribution, allowing mixture weights to be learned.
45. Infinite Mixture Model
    • Student T written as a Mixture Model.

" class="reference-link">Transforms

1. Affine
2. Exp
3. Expm1
4. Gumbel
5. Identity
6. InverseTransform (Inverts a transform)
7. Kumaraswamy
8. Log
9. Logit
10. NICE
11. Planar
12. Power
13. Radial
14. Reciprocal
15. Sigmoid
16. SinhArcsinh
17. Softplus
18. Softsign
19. Square
20. Tanh
21. Weibull

" class="reference-link">Criterion

1. Divergences
   1. Cross Entropy
   2. Perplexity
   3. Exponential
   4. Forward KL Divergence
      • P Model -> Sampling (rsample)
      • Q Model -> PDF Function (log_prob)
   5. Reverse KL Divergence
      • P Model -> PDF Function (log_prob)
      • Q Model -> Sampling + PDF Function
   6. Jensen-Shannon Divergence (JS)
      • P Model -> PDF + Sampling
      • Q Model -> PDF + Sampling
2. Adversarial
   1. GAN Loss
   2. MMGAN Loss
   3. WGAN Loss
   4. LSGAN Loss
3. Variational
   1. ELBO
      • Implements SVI with ELBO loss.
      • Requires a Conditional Model to learn, in addition to P and Q models.

" class="reference-link">Models

1. Regression
   1. Linear Regression (Normal)
   2. L1 Regression (Laplace)
   3. Ridge Regression (Normal + Normal Prior on weights) (Bayesian Linear Regression)
   4. Lasso Regression (Normal + Laplace Prior on weights)
   5. Poisson Regression (Poisson)
   6. Negative Binomial Regression (Generalized Poisson)
2. Classification
   1. Logistic Regression (Bernoulli)
   2. Bayesian Logistic Regression (Bernoulli + Normal Prior on weights)
   3. Softmax Regression (Categorical)
   4. Gaussian Naive Bayes
   5. Bernoulli Naive Bayes
   6. Multinomial Naive Bayes
   7. Linear Discriminant Analysis (Shared Covariance)
   8. Gaussian Discriminant Analysis (Multivariate Normal)
3. Clustering
   1. Gaussian Mixture Model
4. Decomposition
   1. Functional PCA
   2. Dynamic SVD Based (can update projection size)
   3. EM PPCA
   4. Variational PPCA
5. Unconstrained Matrix Factorization
6. Generative Adversarial Networks
   1. GAN
   2. MMGAN
   3. WGAN
   4. LSGAN
7. Variational Auto-Encoder (VAE)
8. Ordinal Models (For Ordinal Targets)
   1. OrdinalLayer (Layer to convert Real Value to Target Prob)
   2. OrdinalModel (Wraps a Predictor + Ordinal in one module)
   3. OrdinalLoss (Reminder to use NLLLoss b/c you don’t want to softmax the probs)
   4. Functional CDFs
      1. exp_cdf -> Exponential Function
      2. erf_cdf -> Error Function as a CDF
      3. tanh_cdf -> Uses Hyperbolic Tangent to fake a CDF
   5. Distribution CDFs
      1. normal_cdf
      2. laplace_cdf
      3. cauchy_cdf

" class="reference-link">Monte Carlo

1. Approximations (Integration, Expectation, Variance, etc.)
2. Inverse Transform Sampling
3. Rejection Sampling (and Mode Sampling)
4. Metropolis
5. Metropolis-Hastings
6. Simulated Annealing
7. Metropolis-Adjusted Langevin Algorithm (MALA)
8. Hamiltonian Monte Carlo (HMC)