lambda-happy 0.1.7

Python package exposing the LambdaHappy class

Lambda Happy

A high-performance CPU/GPU solver for estimating the lambda_happy factor in sparse linear models (≈99% sparsity) using C++/CUDA and PyTorch.

Installation

# Core functionality
pip install lambda-happy

# Benchmark GUI (PyQt5)
pip install lambda-happy[benchmark]

# Validation tools (PyQt5 + pandas)
pip install lambda-happy[validation]

# All extras (Benchmark + Validation tools)
pip install lambda-happy[all]

Then install torch (see: https://pytorch.org/get-started/locally/)

Here is the current command in August 2025 for Linux :

pip3 install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cu118

What is lambda happy ?

In sparse regression, lambda_happy balances data fidelity against model sparsity.

Given:

• X ∈ R -> The feature matrix
• Z ∈ R -> A random Gaussian projection matrix
• Z_centrer -> centered Z matrix

Lambda_happy is estimated as the 95th percentile of (norm of the transpose of X times the centered Z matrix, measured in Chebyshev norm) divided by (norm of the centered Z matrix measured in 2-norm), that is:

• lambda_happy = Quantile_0.95 ( || X^T * Z_centrer ||_infinity / || Z_centrer ||_2 )

which requires:

• p: The number of feature in The feature matrix X (affects only the matmul)
• n: The number of row in The feature matrix x
• m: number of projections (larger m ⇒ higher precision, but each step’s cost scales with m)

Quickstart

import torch
from lambda_happy import LambdaHappy

# Prepare data
X = torch.randn(1000, 5000, device="cuda")

# Initialize solver (auto‐select fastest backend)
solver = LambdaHappy(X, force_fastest=True)

# Single estimate
lambda_value = solver.compute(m=10000)
print(f"lambda_value ≈ {lambda_value:.4f}")

# Multiple runs
lambda_values = solver.compute_many(m=10000, nb_run=50)

# Aggregated (mean)
lambda_mean = solver.compute_agg(m=10000, nb_run=500, func=torch.median)

Performance Trade-Offs

Projection Dimension (m)

• ↑ m → improves lambda_happy precision.
• ↑ m → linearly increases compute time (all kernels scale with m).
• Recommended: m = 10,000 provides good accuracy in most cases.

ℹ️ Use float16 on GPU only if the input matrix X is normalized.
Otherwise, lambda_happy estimation may be unstable or inconsistent.

Sample Dimension (n)

• ↑ n → increases cost in all kernels (since Z ∈ R^(n × m)), except for the quantile post-processing step.

Feature Dimension (p)

• ↑ p → only affects the X^T·Z matrix multiplication.

---

Recommended Settings

Context	Data Type	Notes
CPU	float32	Stable, widely supported, and generally the fastest on CPU.
CUDA GPU	float16	High performance if X is normalized; otherwise use float32.
Backend	"AUTOMATIC"	Selects the best available implementation based on hardware and dtype.

Extras

Benchmark

The lambda-happy-benchmark script measures and compares the performance of LambdaHappy on CPU and GPU. It offers various benchmarking options and displays live throughput plots. Example usage:

lambda-happy-benchmark --benchmark_2D --benchmark_3D --device cuda --dtype float16 -n 1000 -p 1000 -m 10000

This runs a 2D benchmark using CUDA with specified matrix dimensions and then run a 3D benchmark.

ℹ️ Note: Not all hyperparameters are used for every plot, but if provided, they will be applied when relevant.

Validation

The lambda-happy-validation script runs tests to validate lambda_happy estimation accuracy. It generates detailed reports and distribution plots using pandas and PyQt5.

Example usage:

lambda-happy-validation --distribution_small --device cuda --dtype float32 -n 1000 -p 1000

This plots small-scale lambda_happy distributions on cuda for the given parameters.

Results

Here are the results for a CUDA calculation :

Rang	Mode	Version	Précision	FPS	Speed-up
1	Mono-GPU	SMART_TENSOR	Float32	449	1.00x
2	Mono-GPU	GPU_DEDICATED	Float32	501	1.12x
3	Multi-GPU	SMART_TENSOR	Float32	511	1.14x
4	Multi-GPU	SMART_TENSOR	Float16	664	1.48x
5	Multi-GPU	GPU_DEDICATED	Float32	911	2.03x
6	Mono-GPU	SMART_TENSOR	Float16	1'215	2.71x
7	Mono-GPU	GPU_DEDICATED	Float16	1'618	3.60x
8	Multi-GPU	GPU_DEDICATED	Float16	2'104	4.69x

The test server is equipped with an Intel Xeon E5-2699 v3 processor (2014) and three NVIDIA GeForce RTX 2080 Ti graphics cards (2018).

It uses the default parameters for the evaluation with X of size 1000x1000 and m=10000.

ℹ️ Note: Use device="cuda" when you create X.

About This Project

This package is developed as part of the Bachelor’s thesis by Yerly Sevan at HE-Arc, supervised by Cédric Bilat.

For questions or contact: [e-mail]

Lambda Happy

A high-performance CPU/GPU solver for estimating the lambda_happy factor in sparse linear models (≈99% sparsity) using C++/CUDA and PyTorch, compatible with linux only and python 3.10.

Installation

# Core functionality
pip install lambda-happy

# Benchmark GUI (PyQt5)
pip install lambda-happy[benchmark]

# Validation tools (PyQt5 + pandas)
pip install lambda-happy[validation]

# All extras (Benchmark + Validation tools)
pip install lambda-happy[all]

Then install torch (see: https://pytorch.org/get-started/locally/)

pip3 install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cu118

Quickstart

import torch
from lambda_happy import LambdaHappy

# Prepare data
X = torch.randn(1000, 5000, device="cuda")
# Initialize solver (auto‐select fastest backend)
solver = LambdaHappy(X, force_fastest=True)

# Single estimate
λ = solver.compute(m=5000)
print(f"λ ≈ {λ:.4f}")

# Multiple runs
λs = solver.compute_many(m=5000, nb_run=50)

# Aggregated (mean)
λ_mean = solver.compute_agg(m=5000, nb_run=50, func=torch.mean)

What is lambda happy ?

In sparse model, lambda_happy balances data fidelity against model sparsity.

Given:

• X ∈ R -> The feature matrix
• Z ∈ R -> A random Gaussian projection matrix
• Z_centrer -> centered Z matrix

Lambda_happy is estimated as the 95th percentile of (norm of the transpose of X times the centered Z matrix, measured in Chebyshev norm) divided by (norm of the centered Z matrix measured in 2-norm), that is:

• lambda_happy = Quantile_0.95 ( || X^T * Z_centrer ||_infinity / || Z_centrer ||_2 )

which requires:

• p: The number of feature in The feature matrix X (affects only the matmul)
• n: The number of row in The feature matrix x
• m: number of projections (larger m ⇒ higher precision, but each step’s cost scales with m)

Performance Trade-Offs

Projection Dimension (m)

• ↑ m → improves lambda_happy precision.
• ↑ m → linearly increases compute time (all kernels scale with m).
• Recommended: m = 10,000 provides good accuracy in most cases.

ℹ️ Use float16 on GPU only if the input matrix X is normalized.
Otherwise, lambda_happy estimation may be unstable or inconsistent.

Sample Dimension (n)

• ↑ n → increases cost in all kernels (since Z ∈ R^(n × m)), except for the quantile post-processing step.

Feature Dimension (p)

• ↑ p → only affects the X^T·Z matrix multiplication.

---

Recommended Settings

Context	Data Type	Notes
CPU	float32	Stable, widely supported, and generally the fastest on CPU.
CUDA GPU	float16	High performance if X is normalized; otherwise use float32.
Backend	"AUTOMATIC"	Selects the best available implementation based on hardware and dtype.

Extras

Benchmark

The lambda-happy-benchmark script measures and compares the performance of LambdaHappy on CPU and GPU. It offers various benchmarking options and displays live throughput plots. Example usage:

lambda-happy-benchmark --benchmark_2D --benchmark_3D --device cuda --dtype float16 -n 1000 -p 1000 -m 10000

This runs a 2D benchmark using CUDA with specified matrix dimensions and then run a 3D benchmark.

ℹ️ Note: Not all hyperparameters are used for every plot, but if provided, they will be applied when relevant.

Validation

The lambda-happy-validation script runs tests to validate lambda_happy estimation accuracy. It generates detailed reports and distribution plots using pandas and PyQt5.

Example usage:

lambda-happy-validation --distribution_small --device cuda --dtype float32 -n 1000 -p 1000

This plots small-scale lambda_happy distributions on cuda for the given parameters.

Results

Here are the results for a CUDA calculation :

Rang	Mode	Version	Précision	FPS	Speed-up
1	Mono-GPU	SMART_TENSOR	Float32	449	1.00x
2	Mono-GPU	GPU_DEDICATED	Float32	501	1.12x
3	Multi-GPU	SMART_TENSOR	Float32	511	1.14x
4	Multi-GPU	SMART_TENSOR	Float16	664	1.48x
5	Multi-GPU	GPU_DEDICATED	Float32	911	2.03x
6	Mono-GPU	SMART_TENSOR	Float16	1'215	2.71x
7	Mono-GPU	GPU_DEDICATED	Float16	1'618	3.60x
8	Multi-GPU	GPU_DEDICATED	Float16	2'104	4.69x

ℹ️ FPS : number of times the lambda_happy factor is estimated per second.

The test server is equipped with an Intel Xeon E5-2699 v3 processor (2014) and three NVIDIA GeForce RTX 2080 Ti graphics cards (2018).

It uses the default parameters for the evaluation with X of size 1000x1000 and m=10000.

ℹ️ Note: Use device="cuda" when you create X.

About This Project

This package is developed as part of the Bachelor’s thesis by Yerly Sevan at HE-Arc, supervised by Cédric Bilat.

This package, including performance optimizations, was developed as part of a Bachelor’s thesis at HE-Arc by Yerly Sevan ([e-mail]), under the supervision of Cédric Bilat ([e-mail]). The mathematical foundations were developed by Sylvain Sardy ([e-mail]).

For questions or contact: [e-mail] or [e-mail]