sample-complexity

Code for paper "Efficient Sparse Coding using Hierarchical Riemannian Pursuit," in IEEE Transactions on Signal Processing, Y. Xue, V. K. N. Lau and S. Cai, doi: 10.1109/TSP.2021.3093769.

We analyze algorithms to learn Gaussian Bayesian networks with known structure up to a bounded error in total variation distance.

OSRL (Optimal Representation Learning in Multi-Task Bandits) comprises an algorithm that addresses the problem of sample complexity with fixed confidence in Multi-Task Bandit problems. Published at the Thirty-Seventh AAAI Conference on Artificial Intelligence (AAAI23)

Paper and verification code: a single-copy lower bound for rank-one nonlinear overlap estimation

Python implementation of algorithms for Best Policy Identification in Markov Decision Processes

Sharp robustness criteria and optimal certification costs for quantum operations from finite pure-state training sets.

Reproduction code for the paper 'Structure, Not Size: The Sample and Parameter Complexity of State Tracking in Selective State-Space Models' (selective PD-SSM / diagonal SSM / GRU state-tracking, MLX).

Optimal dimension-dependent sample cost of short-time Lindblad simulation, with a universal converse and an explicit collective rank-one processor.

Exact classifiers and rank-dependent sample-complexity bounds for quantum learning from unknown subspace states.

Exact retained-qubit frontier for quantum complement sampling, with optimal decoders, converse bounds, source constructions, and dephasing analysis.

Quantum algorithms for estimating discrete geometric phases from copies of unknown pure states, with dimension-independent copy bounds, coherent loop transport, and minimax lower bounds matching up to logarithmic factors in a specified regime.

An MLP hits a real sample-complexity wall learning sparse parities, with a Fourier-basis progress measure that sees it coming before the loss does

This package was the result of master thesis that is seen at link https://tede2.uepg.br/jspui/handle/prefix/152 and in the article https://doi.org/10.5335/rbca.2015.3727.

Known-state quantum certification under noisy local readout: adaptive sample-complexity bounds, a sharp binary exponent, and fidelity noise thresholds.

Matching high-dimensional copy bounds for pure-state root-fidelity estimation under complete quantum resets, including a converse for adaptive protocols and a finite-precision collective-measurement construction.

Finite-sample guarantees and reproducible experiments for MARVEL/L-MARVEL and PC-style causal discovery

Optimal outcome counts, polynomial rigidity, and statistical costs of universal entanglement detection using fixed collective quantum measurements.

This project dives into mathematical foundations of PAC learning theory while adding Python examples that make core ideas like generalization, sample complexity, VC dimension, halfspaces, perceptrons, and logical semantics executable and easier to inspect.

Copy-complexity separation between quantum conditional-state synthesis and arbitrary classical descriptions, with stabilizer proofs, finite verification, and a Watrous-based learning route.

Project page for our paper on adaptive quantum tomography under Pauli basis measurements.