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Parsa Moradi

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3 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

Adversarial Robustness of Nonparametric Regression

Parsa Moradi
Hanzaleh Nodehi
Mohammad Maddah-Ali

In this paper, we investigate the adversarial robustness of nonparametric regression, a fundamental problem in machine learning, under the setting where an adversary can arbitrarily corrupt a subset of the input data. While the robustness of parametric regression has been extensively studied, its nonparametric counterpart remains largely unexplored. We characterize the adversarial robustness in nonparametric regression, assuming the regression function belongs to the second-order Sobolev space (i. e. , it is square integrable up to its second derivative). The contribution of this paper is two-fold: (i) we establish a minimax lower bound on the estimation error, revealing a fundamental limit that no estimator can overcome, and (ii) we show that, perhaps surprisingly, the classical smoothing spline estimator, when properly regularized, exhibits robustness against adversarial corruption. These results imply that if $o(n)$ out of $n$ samples are corrupted, the estimation error of the smoothing spline vanishes as $n \to \infty$. On the other hand, when a constant fraction of the data is corrupted, no estimator can guarantee vanishing estimation error, implying the optimality of the smoothing spline in terms of maximum tolerable number of corrupted samples.

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NeurIPS Conference 2024 Conference Paper

Coded Computing for Resilient Distributed Computing: A Learning-Theoretic Framework

Parsa Moradi
Behrooz Tahmasebi
Mohammad A. Maddah-Ali

Coded computing has emerged as a promising framework for tackling significant challenges in large-scale distributed computing, including the presence of slow, faulty, or compromised servers. In this approach, each worker node processes a combination of the data, rather than the raw data itself. The final result then is decoded from the collective outputs of the worker nodes. However, there is a significant gap between current coded computing approaches and the broader landscape of general distributed computing, particularly when it comes to machine learning workloads. To bridge this gap, we propose a novel foundation for coded computing, integrating the principles of learning theory, and developing a framework that seamlessly adapts with machine learning applications. In this framework, the objective is to find the encoder and decoder functions that minimize the loss function, defined as the mean squared error between the estimated and true values. Facilitating the search for the optimum decoding and functions, we show that the loss function can be upper-bounded by the summation of two terms: the generalization error of the decoding function and the training error of the encoding function. Focusing on the second-order Sobolev space, we then derive the optimal encoder and decoder. We show that in the proposed solution, the mean squared error of the estimation decays with the rate of $\mathcal{O}(S^3 N^{-3})$ and $\mathcal{O}(S^{\frac{8}{5}}N^{\frac{-3}{5}})$ in noiseless and noisy computation settings, respectively, where $N$ is the number of worker nodes with at most $S$ slow servers (stragglers). Finally, we evaluate the proposed scheme on inference tasks for various machine learning models and demonstrate that the proposed framework outperforms the state-of-the-art in terms of accuracy and rate of convergence.

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ICLR Conference 2020 Conference Paper

Memory-Based Graph Networks

Amir Hosein Khas Ahmadi
Kaveh Hassani
Parsa Moradi
Leo Lee
Quaid Morris

Graph neural networks (GNNs) are a class of deep models that operate on data with arbitrary topology represented as graphs. We introduce an efficient memory layer for GNNs that can jointly learn node representations and coarsen the graph. We also introduce two new networks based on this layer: memory-based GNN (MemGNN) and graph memory network (GMN) that can learn hierarchical graph representations. The experimental results shows that the proposed models achieve state-of-the-art results in eight out of nine graph classification and regression benchmarks. We also show that the learned representations could correspond to chemical features in the molecule data.

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