Erfan Mirzaei

Giacomo Turri, Grégoire Pacreau, Giacomo Meanti et al.

kooplearn is a machine-learning library that implements linear, kernel, and deep-learning estimators of dynamical operators and their spectral decompositions. kooplearn can model both discrete-time evolution operators (Koopman/Transfer) and continuous-time infinitesimal generators. By learning these operators, users can analyze dynamical systems via spectral methods, derive data-driven reduced-order models, and forecast future states and observables. kooplearn's interface is compliant with the scikit-learn API, facilitating its integration into existing machine learning and data science workflows. Additionally, kooplearn includes curated benchmark datasets to support experimentation, reproducibility, and the fair comparison of learning algorithms. The software is available at https://github.com/Machine-Learning-Dynamical-Systems/kooplearn.

Erfan Mirzaei, Seyed Pooya Shariatpanahi, Alireza Tavakoli et al.

Personalized AI-based services involve a population of individual reinforcement learning agents. However, most reinforcement learning algorithms focus on harnessing individual learning and fail to leverage the social learning capabilities commonly exhibited by humans and animals. Social learning integrates individual experience with observing others' behavior, presenting opportunities for improved learning outcomes. In this study, we focus on a social bandit learning scenario where a social agent observes other agents' actions without knowledge of their rewards. The agents independently pursue their own policy without explicit motivation to teach each other. We propose a free energy-based social bandit learning algorithm over the policy space, where the social agent evaluates others' expertise levels without resorting to any oracle or social norms. Accordingly, the social agent integrates its direct experiences in the environment and others' estimated policies. The theoretical convergence of our algorithm to the optimal policy is proven. Empirical evaluations validate the superiority of our social learning method over alternative approaches in various scenarios. Our algorithm strategically identifies the relevant agents, even in the presence of random or suboptimal agents, and skillfully exploits their behavioral information. In addition to societies including expert agents, in the presence of relevant but non-expert agents, our algorithm significantly enhances individual learning performance, where most related methods fail. Importantly, it also maintains logarithmic regret.

Andreas Maurer, Erfan Mirzaei, Massimiliano Pontil

The paper provides data-dependent bounds on the test error of the Gibbs algorithm in the overparameterized interpolation regime, where low training errors are also obtained for impossible data, such as random labels in classification. The bounds are stable under approximation with Langevin Monte Carlo algorithms. Experiments on the MNIST and CIFAR-10 datasets verify that the bounds yield nontrivial predictions on true labeled data and correctly upper bound the test error for random labels. Our method indicates that generalization in the low-temperature, interpolation regime is already signaled by small training errors in the more classical high temperature regime.

Erfan Mirzaei, Andreas Maurer, Vladimir R. Kostic et al.

Learning from non-independent and non-identically distributed data poses a persistent challenge in statistical learning. In this study, we introduce data-dependent Bernstein inequalities tailored for vector-valued processes in Hilbert space. Our inequalities apply to both stationary and non-stationary processes and exploit the potential rapid decay of correlations between temporally separated variables to improve estimation. We demonstrate the utility of these bounds by applying them to covariance operator estimation in the Hilbert-Schmidt norm and to operator learning in dynamical systems, achieving novel risk bounds. Finally, we perform numerical experiments to illustrate the practical implications of these bounds in both contexts.

Hafez Ghaemi, Erfan Mirzaei, Mahbod Nouri et al.

Brain-inspired computation and information processing alongside compatibility with neuromorphic hardware have made spiking neural networks (SNN) a promising method for solving learning tasks in machine learning (ML). Spiking neurons are only one of the requirements for building a bio-plausible learning model. Network architecture and learning rules are other important factors to consider when developing such artificial agents. In this work, inspired by the human visual pathway and the role of dopamine in learning, we propose a reward-modulated locally connected spiking neural network, BioLCNet, for visual learning tasks. To extract visual features from Poisson-distributed spike trains, we used local filters that are more analogous to the biological visual system compared to convolutional filters with weight sharing. In the decoding layer, we applied a spike population-based voting scheme to determine the decision of the network. We employed Spike-timing-dependent plasticity (STDP) for learning the visual features, and its reward-modulated variant (R-STDP) for training the decoder based on the reward or punishment feedback signal. For evaluation, we first assessed the robustness of our rewarding mechanism to varying target responses in a classical conditioning experiment. Afterwards, we evaluated the performance of our network on image classification tasks of MNIST and XOR MNIST datasets.