Valid Inference
95% confidence intervals that actually cover 95% of the time
13 Model Families
Linear, Logit, Poisson, Gamma, NegBin, Weibull, Gumbel, Tobit, Gaussian, Probit, Beta, ZIP, Multinomial Logit
Economic Targets
AME, Elasticity, WTP, Dose-Response, Profit, Consumer Welfare, Conditional Variance, and custom targets with autodiff
Regime Detection
Auto-selects optimal Lambda strategy for RCTs vs observational data
PyTorch Backend
Automatic differentiation for exact gradients and Hessians
```
## Quick Start
```python
import numpy as np
import torch
from deep_inference import structural_dml
# Heterogeneous logistic demand (binary outcomes)
np.random.seed(42)
torch.manual_seed(42)
n = 2000
X = np.random.randn(n, 5)
T = np.random.randn(n)
# Heterogeneous treatment effect: β(X) = 0.5 + 0.3*X₁
alpha = 0.2 * X[:, 0]
beta = 0.5 + 0.3 * X[:, 1]
prob = 1 / (1 + np.exp(-(alpha + beta * T)))
Y = np.random.binomial(1, prob).astype(float)
# Run influence function inference
result = structural_dml(
Y=Y, T=T, X=X,
family='logit',
hidden_dims=[64, 32],
epochs=100,
n_folds=50
)
print(result.summary())
```
**Output** (Date/Time will vary):
```
==============================================================================
Structural DML Results
==============================================================================
Family: Logit Target: E[beta]
No. Observations: 2000 No. Folds: 50
Date: Fri, 16 Jan 2026 Time: 13:54:12
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
E[beta] 0.4704 0.0496 9.492 0.000 0.3733 0.5675
==============================================================================
Diagnostics:
Min Lambda eigenvalue: 0.134946
Mean condition number: 1.17
Correction ratio: 45.2493
Pct regularized: 0.0%
------------------------------------------------------------------------------
```
### Predictions & Visualization
```python
# Predict treatment effects for new observations
X_new = np.random.randn(5, 5)
beta_new = result.predict_beta(X_new)
print(f"Predicted β(X) for new data: {beta_new}")
# Predict probabilities at treatment level T=1
proba = result.predict_proba(X_new, t_value=1.0)
print(f"P(Y=1|X,T=1): {proba}")
# Visualize heterogeneity distributions
result.plot_distributions()
result.plot_heterogeneity(feature_idx=1) # β(X) vs X₁
```
**Distribution of estimated parameters:**
**Treatment effect heterogeneity (β vs X₁):**
## Economic Targets
The `inference()` API supports built-in economic targets:
```python
from deep_inference import inference
# Built-in: average marginal effect
result = inference(Y, T, X, model='logit', target='ame', t_tilde=0.0)
print(result.summary())
```
The same target can be defined from scratch with a custom loss and custom target — autodiff handles all derivatives:
```python
import torch
# Custom loss (logit negative log-likelihood)
def my_loss(y, t, theta):
p = torch.sigmoid(theta[0] + theta[1] * t)
return -y * torch.log(p + 1e-7) - (1 - y) * torch.log(1 - p + 1e-7)
# Custom target (average marginal effect at t_tilde)
def my_ame(x, theta, t_tilde):
p = torch.sigmoid(theta[0] + theta[1] * t_tilde)
return p * (1 - p) * theta[1]
result = inference(Y, T, X, loss=my_loss, target_fn=my_ame, theta_dim=2, t_tilde=0.0)
```
**Built-in output** (Date/Time will vary):
```
==============================================================================
Structural Inference Results
==============================================================================
Family: Logit Target: ame
No. Observations: 2000 No. Folds: 50
Date: Sat, 07 Feb 2026 Time: 23:37:29
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
ame 0.1181 0.0127 9.290 0.000 0.0932 0.1431
==============================================================================
Diagnostics:
------------------------------------------------------------------------------
```
**Custom output**:
```
==============================================================================
Structural Inference Results
==============================================================================
No. Observations: 2000 Target: E[beta]
Date: Sat, 07 Feb 2026 No. Folds: 50
Time: 23:41:09
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
E[beta] 0.1251 0.0128 9.763 0.000 0.1000 0.1502
==============================================================================
Diagnostics:
------------------------------------------------------------------------------
```
> Both approaches produce matching estimates (0.118 vs 0.125, within MC noise). Output generated by [`docs/generate_quickstart_plots.py`](https://github.com/rawatpranjal/deep-inference/blob/main/docs/generate_quickstart_plots.py).
More built-in targets:
```python
# Price elasticity at P=2.0
result = inference(Y, T, X, model='logit', target='elasticity', t_tilde=2.0)
# Consumer welfare
result = inference(Y, T, X, model='logit', target='welfare', t_tilde=2.0)
# Dose-response: average predicted outcome at treatment level
result = inference(Y, T, X, model='logit', target='dose_response', t_tilde=1.0)
# Expected profit/revenue at price level
result = inference(Y, T, X, model='logit', target='profit', t_tilde=2.0)
# Conditional variance (risk heterogeneity)
result = inference(Y, T, X, model='logit', target='conditional_variance', t_tilde=0.0)
# Randomized experiment (compute Lambda instead of estimating)
from deep_inference.lambda_.compute import Normal
result = inference(Y, T, X, model='logit', target='beta',
is_randomized=True, treatment_dist=Normal(0, 1))
```
## Why deep-inference?
**The Problem**: Neural networks are great at prediction but naive inference produces invalid confidence intervals with coverage far below 95%.
**The Solution**: Influence function-based debiasing corrects for regularization bias, providing valid confidence intervals for economic targets like average treatment effects.
| Method | Coverage | SE Ratio |
|--------|----------|----------|
| Naive | 8% | 0.27 |
| **Influence** | **95%** | **1.08** |
## Documentation
```{toctree}
:maxdepth: 2
:caption: Contents
getting_started/index
flowchart
tutorials/index
theory/index
algorithm/index
validation/index
api/index
```
## References
### Core Framework
- Farrell, Liang, Misra (2021): "Deep Neural Networks for Estimation and Inference" *Econometrica* ([pdf](references/FLM2021_docling.md))
- Farrell, Liang, Misra (2025): "Deep Learning for Individual Heterogeneity" *Working Paper* ([pdf](references/FLM2025_docling.md))
### Applications
- Dubé, Misra (2023): "Personalized Pricing and Consumer Welfare" *Journal of Political Economy* ([pdf](references/DM2023_docling.md))
- Hetzenecker, Osterhaus (2024): "Deep Learning for Heterogeneous Parameters in Discrete Choice Models" *arXiv 2408.09560* ([pdf](references/HO2024_multinomial_docling.md))
- Colangelo, Lee (2026): "Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments" *JBES* ([pdf](references/CL2026_docling.md))
- Momin (2025): "Heterogeneous Treatment Effects and Counterfactual Policy Targeting Using Deep Neural Networks" *SSRN 5149650*
- Chen, Liu, Ma, Zhang (2024): "Causal Inference of General Treatment Effects using Neural Networks" *Journal of Econometrics* ([pdf](references/CLMZ2024_docling.md))
- Ye, Zhang, Zhang, Zhang, Zhang (2025): "Deep-Learning-Based Causal Inference for Large-Scale Combinatorial Experiments" *Management Science* ([pdf](references/DeDL2025_docling.md))
### Automatic Debiasing / Riesz Representation
- Chernozhukov, Newey, Quintas-Martinez, Syrgkanis (2022): "RieszNet and ForestRiesz: Automatic Debiased Machine Learning with Neural Nets" *ICML* ([pdf](references/RieszNet2022_docling.md))
- Chernozhukov, Newey, Singh (2022): "Automatic Debiased Machine Learning of Causal and Structural Effects" *Econometrica* ([pdf](references/CNSS2020_adversarial_riesz_docling.md))
- Chernozhukov, Newey, Quintas-Martinez, Syrgkanis (2021): "Automatic Debiased Machine Learning via Neural Nets for Generalized Linear Regression" *Working Paper* ([pdf](references/IN_glr_docling.md))
- Hines, Hines (2025): "Automatic Debiasing of Neural Networks via Moment-Constrained Learning" *CLeaR* ([pdf](references/HH2025_docling.md))
### DNN Architecture + Influence Functions
- Shi, Blei, Veitch (2019): "Adapting Neural Networks for the Estimation of Treatment Effects" *NeurIPS* ([pdf](references/Dragonnet2019_docling.md))
- Li, McCoy et al. (2025): "Targeted Deep Architectures for Estimation and Inference" *arXiv 2507.12435* ([pdf](references/TDA2025_docling.md))
- Shirakawa et al. (2024): "Deep Longitudinal Targeted Minimum Loss-based Estimation" *ICML* ([pdf](references/DeepLTMLE2024_docling.md))
- Liu et al. (2024): "DNA-SE: Towards Deep Neural-Nets Assisted Semiparametric Estimation" *ICML* ([pdf](references/DNASE2024_docling.md))
- Cai, Fonseca, Hou, Namkoong (2025): "C-Learner: Constrained Learning for Causal Inference and Semiparametric Statistics" *arXiv 2405.09493* ([pdf](references/CLearner2025_docling.md))
### Theory
- Yan, Chen, Yao (2025): "Overparameterized Neural Networks in Semiparametric Inference" *arXiv 2504.19089* ([pdf](references/YCY2025_docling.md))
- Metzger (2022): "Adversarial Estimators" *arXiv 2204.10495* ([pdf](references/Metzger2022_docling.md))
- Foster, Syrgkanis (2023): "Orthogonal Statistical Learning" *Annals of Statistics* ([pdf](references/FS2023_docling.md))
### Frontier
- Melnychuk, Feuerriegel (2026): "GDR-Learners: Generalized Doubly Robust Learners for Causal Inference" *ICLR* ([pdf](references/GDR2026_docling.md))
- Nguyen (2025): "Neural Network Estimation and Simulation for Dynamic Discrete Choice Models" *Georgetown JMP* ([pdf](references/NNES2025_docling.md))
## License
MIT License