Simon Luo

Wanchuang Zhu, Benjamin Zi Hao Zhao, Simon Luo et al.

Byzantine attacks hinder the deployment of federated learning algorithms. Although we know that the benign gradients and Byzantine attacked gradients are distributed differently, to detect the malicious gradients is challenging due to (1) the gradient is high-dimensional and each dimension has its unique distribution and (2) the benign gradients and the attacked gradients are always mixed (two-sample test methods cannot apply directly). To address the above, for the first time, we propose MANDERA which is theoretically guaranteed to efficiently detect all malicious gradients under Byzantine attacks with no prior knowledge or history about the number of attacked nodes. More specifically, we transfer the original updating gradient space into a ranking matrix. By such an operation, the scales of different dimensions of the gradients in the ranking space become identical. The high-dimensional benign gradients and the malicious gradients can be easily separated. The effectiveness of MANDERA is further confirmed by experimentation on four Byzantine attack implementations (Gaussian, Zero Gradient, Sign Flipping, Shifted Mean), comparing with state-of-the-art defenses. The experiments cover both IID and Non-IID datasets.

Simon Luo, Feng Zhou, Lamiae Azizi et al.

We present the Additive Poisson Process (APP), a novel framework that can model the higher-order interaction effects of the intensity functions in stochastic processes using lower dimensional projections. Our model combines the techniques in information geometry to model higher-order interactions on a statistical manifold and in generalized additive models to use lower-dimensional projections to overcome the effects from the curse of dimensionality. Our approach solves a convex optimization problem by minimizing the KL divergence from a sample distribution in lower dimensional projections to the distribution modeled by an intensity function in the stochastic process. Our empirical results show that our model is able to use samples observed in the lower dimensional space to estimate the higher-order intensity function with extremely sparse observations.

Harrison Nguyen, Simon Luo, Fabio Ramos

Magnetic Resonance Imaging (MRI) of the brain can come in the form of different modalities such as T1-weighted and Fluid Attenuated Inversion Recovery (FLAIR) which has been used to investigate a wide range of neurological disorders. Current state-of-the-art models for brain tissue segmentation and disease classification require multiple modalities for training and inference. However, the acquisition of all of these modalities are expensive, time-consuming, inconvenient and the required modalities are often not available. As a result, these datasets contain large amounts of \emph{unpaired} data, where examples in the dataset do not contain all modalities. On the other hand, there is smaller fraction of examples that contain all modalities (\emph{paired} data) and furthermore each modality is high dimensional when compared to number of datapoints. In this work, we develop a method to address these issues with semi-supervised learning in translating between two neuroimaging modalities. Our proposed model, Semi-Supervised Adversarial CycleGAN (SSA-CGAN), uses an adversarial loss to learn from \emph{unpaired} data points, cycle loss to enforce consistent reconstructions of the mappings and another adversarial loss to take advantage of \emph{paired} data points. Our experiments demonstrate that our proposed framework produces an improvement in reconstruction error and reduced variance for the pairwise translation of multiple modalities and is more robust to thermal noise when compared to existing methods.

Simon Luo, Lamiae Azizi, Mahito Sugiyama

We present a novel blind source separation (BSS) method, called information geometric blind source separation (IGBSS). Our formulation is based on the log-linear model equipped with a hierarchically structured sample space, which has theoretical guarantees to uniquely recover a set of source signals by minimizing the KL divergence from a set of mixed signals. Source signals, received signals, and mixing matrices are realized as different layers in our hierarchical sample space. Our empirical results have demonstrated on images and time series data that our approach is superior to well established techniques and is able to separate signals with complex interactions.

Simon Luo, Mahito Sugiyama

Hierarchical probabilistic models are able to use a large number of parameters to create a model with a high representation power. However, it is well known that increasing the number of parameters also increases the complexity of the model which leads to a bias-variance trade-off. Although it is a classical problem, the bias-variance trade-off between hidden layers and higher-order interactions have not been well studied. In our study, we propose an efficient inference algorithm for the log-linear formulation of the higher-order Boltzmann machine using a combination of Gibbs sampling and annealed importance sampling. We then perform a bias-variance decomposition to study the differences in hidden layers and higher-order interactions. Our results have shown that using hidden layers and higher-order interactions have a comparable error with a similar order of magnitude and using higher-order interactions produce less variance for smaller sample size.