Richard M. Leahy

LG
h-index73
21papers
243citations
Novelty49%
AI Score53

21 Papers

27.5LGNov 7, 2023Code
Neuro-GPT: Towards A Foundation Model for EEG

Wenhui Cui, Woojae Jeong, Philipp Thölke et al.

To handle the scarcity and heterogeneity of electroencephalography (EEG) data for Brain-Computer Interface (BCI) tasks, and to harness the power of large publicly available data sets, we propose Neuro-GPT, a foundation model consisting of an EEG encoder and a GPT model. The foundation model is pre-trained on a large-scale data set using a self-supervised task that learns how to reconstruct masked EEG segments. We then fine-tune the model on a Motor Imagery Classification task to validate its performance in a low-data regime (9 subjects). Our experiments demonstrate that applying a foundation model can significantly improve classification performance compared to a model trained from scratch, which provides evidence for the generalizability of the foundation model and its ability to address challenges of data scarcity and heterogeneity in EEG. The code is publicly available at github.com/wenhui0206/NeuroGPT.

2.0IVJun 13, 2018
Accelerated Wirtinger Flow: A fast algorithm for ptychography

Rui Xu, Mahdi Soltanolkotabi, Justin P. Haldar et al.

This paper presents a new algorithm, Accelerated Wirtinger Flow (AWF), for ptychographic image reconstruction from phaseless diffraction pattern measurements. AWF is based on combining Nesterov's acceleration approach with Wirtinger gradient descent. Theoretical results enable prespecification of all AWF algorithm parameters, with no need for computationally-expensive line searches and no need for manual parameter tuning. AWF is evaluated in the context of simulated X-ray ptychography, where we demonstrate fast convergence and low per-iteration computational complexity. We also show examples where AWF reaches higher image quality with less computation than classical algorithms. AWF is also shown to have robustness to noise and probe misalignment.

4.8CVAug 26, 2022
Learning From Positive and Unlabeled Data Using Observer-GAN

Omar Zamzam, Haleh Akrami, Richard Leahy

The problem of learning from positive and unlabeled data (A.K.A. PU learning) has been studied in a binary (i.e., positive versus negative) classification setting, where the input data consist of (1) observations from the positive class and their corresponding labels, (2) unlabeled observations from both positive and negative classes. Generative Adversarial Networks (GANs) have been used to reduce the problem to the supervised setting with the advantage that supervised learning has state-of-the-art accuracy in classification tasks. In order to generate \textit{pseudo}-negative observations, GANs are trained on positive and unlabeled observations with a modified loss. Using both positive and \textit{pseudo}-negative observations leads to a supervised learning setting. The generation of pseudo-negative observations that are realistic enough to replace missing negative class samples is a bottleneck for current GAN-based algorithms. By including an additional classifier into the GAN architecture, we provide a novel GAN-based approach. In our suggested method, the GAN discriminator instructs the generator only to produce samples that fall into the unlabeled data distribution, while a second classifier (observer) network monitors the GAN training to: (i) prevent the generated samples from falling into the positive distribution; and (ii) learn the features that are the key distinction between the positive and negative observations. Experiments on four image datasets demonstrate that our trained observer network performs better than existing techniques in discriminating between real unseen positive and negative samples.

6.9LGMar 3, 2022Code
Semi-supervised Learning using Robust Loss

Wenhui Cui, Haleh Akrami, Anand A. Joshi et al.

The amount of manually labeled data is limited in medical applications, so semi-supervised learning and automatic labeling strategies can be an asset for training deep neural networks. However, the quality of the automatically generated labels can be uneven and inferior to manual labels. In this paper, we suggest a semi-supervised training strategy for leveraging both manually labeled data and extra unlabeled data. In contrast to the existing approaches, we apply robust loss for the automated labeled data to automatically compensate for the uneven data quality using a teacher-student framework. First, we generate pseudo-labels for unlabeled data using a teacher model pre-trained on labeled data. These pseudo-labels are noisy, and using them along with labeled data for training a deep neural network can severely degrade learned feature representations and the generalization of the network. Here we mitigate the effect of these pseudo-labels by using robust loss functions. Specifically, we use three robust loss functions, namely beta cross-entropy, symmetric cross-entropy, and generalized cross-entropy. We show that our proposed strategy improves the model performance by compensating for the uneven quality of labels in image classification as well as segmentation applications.

6.6IVAug 8, 2022Code
Learning from imperfect training data using a robust loss function: application to brain image segmentation

Haleh Akrami, Wenhui Cui, Anand A Joshi et al.

Segmentation is one of the most important tasks in MRI medical image analysis and is often the first and the most critical step in many clinical applications. In brain MRI analysis, head segmentation is commonly used for measuring and visualizing the brain's anatomical structures and is also a necessary step for other applications such as current-source reconstruction in electroencephalography and magnetoencephalography (EEG/MEG). Here we propose a deep learning framework that can segment brain, skull, and extra-cranial tissue using only T1-weighted MRI as input. In addition, we describe a robust method for training the model in the presence of noisy labels.

1.8LGDec 16, 2022
Toward Improved Generalization: Meta Transfer of Self-supervised Knowledge on Graphs

Wenhui Cui, Haleh Akrami, Anand A. Joshi et al.

Despite the remarkable success achieved by graph convolutional networks for functional brain activity analysis, the heterogeneity of functional patterns and the scarcity of imaging data still pose challenges in many tasks. Transferring knowledge from a source domain with abundant training data to a target domain is effective for improving representation learning on scarce training data. However, traditional transfer learning methods often fail to generalize the pre-trained knowledge to the target task due to domain discrepancy. Self-supervised learning on graphs can increase the generalizability of graph features since self-supervision concentrates on inherent graph properties that are not limited to a particular supervised task. We propose a novel knowledge transfer strategy by integrating meta-learning with self-supervised learning to deal with the heterogeneity and scarcity of fMRI data. Specifically, we perform a self-supervised task on the source domain and apply meta-learning, which strongly improves the generalizability of the model using the bi-level optimization, to transfer the self-supervised knowledge to the target domain. Through experiments on a neurological disorder classification task, we demonstrate that the proposed strategy significantly improves target task performance by increasing the generalizability and transferability of graph-based knowledge.

5.6LGApr 16
Predicting Post-Traumatic Epilepsy from Clinical Records using Large Language Model Embeddings

Wenhui Cui, Nicholas Swingle, Anand A. Joshi et al.

Objective: Post-traumatic epilepsy (PTE) is a debilitating neurological disorder that develops after traumatic brain injury (TBI). Early prediction of PTE remains challenging due to heterogeneous clinical data, limited positive cases, and reliance on resource-intensive neuroimaging data. We investigate whether routinely collected acute clinical records alone can support early PTE prediction using language model-based approaches. Methods: Using a curated subset of the TRACK-TBI cohort, we developed an automated PTE prediction framework that implements pretrained large language models (LLMs) as fixed feature extractors to encode clinical records. Tabular features, LLM-generated embeddings, and hybrid feature representations were evaluated using gradient-boosted tree classifiers under stratified cross-validation. Results: LLM embeddings achieved performance improvements by capturing contextual clinical information compared to using tabular features alone. The best performance was achieved by a modality-aware feature fusion strategy combining tabular features and LLM embeddings, achieving an AUC-ROC of 0.892 and AUPRC of 0.798. Acute post-traumatic seizures, injury severity, neurosurgical intervention, and ICU stay are key contributors to the predictive performance. Significance: These findings demonstrate that routine acute clinical records contain information suitable for early PTE risk prediction using LLM embeddings in conjunction with gradient-boosted tree classifiers. This approach represents a promising complement to imaging-based prediction.

1.2SPNov 15, 2025Code
Informed Bootstrap Augmentation Improves EEG Decoding

Woojae Jeong, Wenhui Cui, Kleanthis Avramidis et al.

Electroencephalography (EEG) offers detailed access to neural dynamics but remains constrained by noise and trial-by-trial variability, limiting decoding performance in data-restricted or complex paradigms. Data augmentation is often employed to enhance feature representations, yet conventional uniform averaging overlooks differences in trial informativeness and can degrade representational quality. We introduce a weighted bootstrapping approach that prioritizes more reliable trials to generate higher-quality augmented samples. In a Sentence Evaluation paradigm, weights were computed from relative ERP differences and applied during probabilistic sampling and averaging. Across conditions, weighted bootstrapping improved decoding accuracy relative to unweighted (from 68.35% to 71.25% at best), demonstrating that emphasizing reliable trials strengthens representational quality. The results demonstrate that reliability-based augmentation yields more robust and discriminative EEG representations. The code is publicly available at https://github.com/lyricists/NeuroBootstrap.

5.3LGSep 14, 2023
Beta quantile regression for robust estimation of uncertainty in the presence of outliers

Haleh Akrami, Omar Zamzam, Anand Joshi et al.

Quantile Regression (QR) can be used to estimate aleatoric uncertainty in deep neural networks and can generate prediction intervals. Quantifying uncertainty is particularly important in critical applications such as clinical diagnosis, where a realistic assessment of uncertainty is essential in determining disease status and planning the appropriate treatment. The most common application of quantile regression models is in cases where the parametric likelihood cannot be specified. Although quantile regression is quite robust to outlier response observations, it can be sensitive to outlier covariate observations (features). Outlier features can compromise the performance of deep learning regression problems such as style translation, image reconstruction, and deep anomaly detection, potentially leading to misleading conclusions. To address this problem, we propose a robust solution for quantile regression that incorporates concepts from robust divergence. We compare the performance of our proposed method with (i) least trimmed quantile regression and (ii) robust regression based on the regularization of case-specific parameters in a simple real dataset in the presence of outlier. These methods have not been applied in a deep learning framework. We also demonstrate the applicability of the proposed method by applying it to a medical imaging translation task using diffusion models.

2.0LGOct 5, 2023
Learning A Disentangling Representation For PU Learning

Omar Zamzam, Haleh Akrami, Mahdi Soltanolkotabi et al.

In this paper, we address the problem of learning a binary (positive vs. negative) classifier given Positive and Unlabeled data commonly referred to as PU learning. Although rudimentary techniques like clustering, out-of-distribution detection, or positive density estimation can be used to solve the problem in low-dimensional settings, their efficacy progressively deteriorates with higher dimensions due to the increasing complexities in the data distribution. In this paper we propose to learn a neural network-based data representation using a loss function that can be used to project the unlabeled data into two (positive and negative) clusters that can be easily identified using simple clustering techniques, effectively emulating the phenomenon observed in low-dimensional settings. We adopt a vector quantization technique for the learned representations to amplify the separation between the learned unlabeled data clusters. We conduct experiments on simulated PU data that demonstrate the improved performance of our proposed method compared to the current state-of-the-art approaches. We also provide some theoretical justification for our two cluster-based approach and our algorithmic choices.

6.3IVDec 16, 2024Code
Generalizable Representation Learning for fMRI-based Neurological Disorder Identification

Wenhui Cui, Haleh Akrami, Anand A. Joshi et al.

Despite the impressive advances achieved using deep learning for functional brain activity analysis, the heterogeneity of functional patterns and the scarcity of imaging data still pose challenges in tasks such as identifying neurological disorders. For functional Magnetic Resonance Imaging (fMRI), while data may be abundantly available from healthy controls, clinical data is often scarce, especially for rare diseases, limiting the ability of models to identify clinically-relevant features. We overcome this limitation by introducing a novel representation learning strategy integrating meta-learning with self-supervised learning to improve the generalization from normal to clinical features. This approach enables generalization to challenging clinical tasks featuring scarce training data. We achieve this by leveraging self-supervised learning on the control dataset to focus on inherent features that are not limited to a particular supervised task and incorporating meta-learning to improve the generalization across domains. To explore the generalizability of the learned representations to unseen clinical applications, we apply the model to four distinct clinical datasets featuring scarce and heterogeneous data for neurological disorder classification. Results demonstrate the superiority of our representation learning strategy on diverse clinically-relevant tasks. Code is publicly available at https://github.com/wenhui0206/MeTSK/tree/main

10.4LGFeb 15, 2024
Knowledge-guided EEG Representation Learning

Aditya Kommineni, Kleanthis Avramidis, Richard Leahy et al.

Self-supervised learning has produced impressive results in multimedia domains of audio, vision and speech. This paradigm is equally, if not more, relevant for the domain of biosignals, owing to the scarcity of labelled data in such scenarios. The ability to leverage large-scale unlabelled data to learn robust representations could help improve the performance of numerous inference tasks on biosignals. Given the inherent domain differences between multimedia modalities and biosignals, the established objectives for self-supervised learning may not translate well to this domain. Hence, there is an unmet need to adapt these methods to biosignal analysis. In this work we propose a self-supervised model for EEG, which provides robust performance and remarkable parameter efficiency by using state space-based deep learning architecture. We also propose a novel knowledge-guided pre-training objective that accounts for the idiosyncrasies of the EEG signal. The results indicate improved embedding representation learning and downstream performance compared to prior works on exemplary tasks. Also, the proposed objective significantly reduces the amount of pre-training data required to obtain performance equivalent to prior works.

10.4IVDec 21, 2023
Meta Transfer of Self-Supervised Knowledge: Foundation Model in Action for Post-Traumatic Epilepsy Prediction

Wenhui Cui, Haleh Akrami, Ganning Zhao et al.

Despite the impressive advancements achieved using deep-learning for functional brain activity analysis, the heterogeneity of functional patterns and scarcity of imaging data still pose challenges in tasks such as prediction of future onset of Post-Traumatic Epilepsy (PTE) from data acquired shortly after traumatic brain injury (TBI). Foundation models pre-trained on separate large-scale datasets can improve the performance from scarce and heterogeneous datasets. For functional Magnetic Resonance Imaging (fMRI), while data may be abundantly available from healthy controls, clinical data is often scarce, limiting the ability of foundation models to identify clinically-relevant features. We overcome this limitation by introducing a novel training strategy for our foundation model by integrating meta-learning with self-supervised learning to improve the generalization from normal to clinical features. In this way we enable generalization to other downstream clinical tasks, in our case prediction of PTE. To achieve this, we perform self-supervised training on the control dataset to focus on inherent features that are not limited to a particular supervised task while applying meta-learning, which strongly improves the model's generalizability using bi-level optimization. Through experiments on neurological disorder classification tasks, we demonstrate that the proposed strategy significantly improves task performance on small-scale clinical datasets. To explore the generalizability of the foundation model in downstream applications, we then apply the model to an unseen TBI dataset for prediction of PTE using zero-shot learning. Results further demonstrated the enhanced generalizability of our foundation model.

16.9LGOct 10, 2025
Neural Codecs as Biosignal Tokenizers

Kleanthis Avramidis, Tiantian Feng, Woojae Jeong et al.

Neurophysiological recordings such as electroencephalography (EEG) offer accessible and minimally invasive means of estimating physiological activity for applications in healthcare, diagnostic screening, and even immersive entertainment. However, these recordings yield high-dimensional, noisy time-series data that typically require extensive pre-processing and handcrafted feature extraction to reveal meaningful information. Recently, there has been a surge of interest in applying representation learning techniques from large pre-trained (foundation) models to effectively decode and interpret biosignals. We discuss the challenges posed for incorporating such methods and introduce BioCodec, an alternative representation learning framework inspired by neural codecs to capture low-level signal characteristics in the form of discrete tokens. Pre-trained on thousands of EEG hours, BioCodec shows efficacy across multiple downstream tasks, ranging from clinical diagnostic tasks and sleep physiology to decoding speech and motor imagery, particularly in low-resource settings. Additionally, we provide a qualitative analysis of codebook usage and estimate the spatial coherence of codebook embeddings from EEG connectivity. Notably, we also document the suitability of our method to other biosignal data, i.e., electromyographic (EMG) signals. Overall, the proposed approach provides a versatile solution for biosignal tokenization that performs competitively with state-of-the-art models. The source code and model checkpoints are shared.

3.6CVJul 8, 2025
Modeling and Reversing Brain Lesions Using Diffusion Models

Omar Zamzam, Haleh Akrami, Anand Joshi et al.

Brain lesions are abnormalities or injuries in brain tissue that are often detectable using magnetic resonance imaging (MRI), which reveals structural changes in the affected areas. This broad definition of brain lesions includes areas of the brain that are irreversibly damaged, as well as areas of brain tissue that are deformed as a result of lesion growth or swelling. Despite the importance of differentiating between damaged and deformed tissue, existing lesion segmentation methods overlook this distinction, labeling both of them as a single anomaly. In this work, we introduce a diffusion model-based framework for analyzing and reversing the brain lesion process. Our pipeline first segments abnormal regions in the brain, then estimates and reverses tissue deformations by restoring displaced tissue to its original position, isolating the core lesion area representing the initial damage. Finally, we inpaint the core lesion area to arrive at an estimation of the pre-lesion healthy brain. This proposed framework reverses a forward lesion growth process model that is well-established in biomechanical studies that model brain lesions. Our results demonstrate improved accuracy in lesion segmentation, characterization, and brain labeling compared to traditional methods, offering a robust tool for clinical and research applications in brain lesion analysis. Since pre-lesion healthy versions of abnormal brains are not available in any public dataset for validation of the reverse process, we simulate a forward model to synthesize multiple lesioned brain images.

7.1LGApr 29, 2025
Deep Learning Characterizes Depression and Suicidal Ideation from Eye Movements

Kleanthis Avramidis, Woojae Jeong, Aditya Kommineni et al.

Identifying physiological and behavioral markers for mental health conditions is a longstanding challenge in psychiatry. Depression and suicidal ideation, in particular, lack objective biomarkers, with screening and diagnosis primarily relying on self-reports and clinical interviews. Here, we investigate eye tracking as a potential marker modality for screening purposes. Eye movements are directly modulated by neuronal networks and have been associated with attentional and mood-related patterns; however, their predictive value for depression and suicidality remains unclear. We recorded eye-tracking sequences from 126 young adults as they read and responded to affective sentences, and subsequently developed a deep learning framework to predict their clinical status. The proposed model included separate branches for trials of positive and negative sentiment, and used 2D time-series representations to account for both intra-trial and inter-trial variations. We were able to identify depression and suicidal ideation with an area under the receiver operating curve (AUC) of 0.793 (95% CI: 0.765-0.819) against healthy controls, and suicidality specifically with 0.826 AUC (95% CI: 0.797-0.852). The model also exhibited moderate, yet significant, accuracy in differentiating depressed from suicidal participants, with 0.609 AUC (95% CI 0.571-0.646). Discriminative patterns emerge more strongly when assessing the data relative to response generation than relative to the onset time of the final word of the sentences. The most pronounced effects were observed for negative-sentiment sentences, that are congruent to depressed and suicidal participants. Our findings highlight eye tracking as an objective tool for mental health assessment and underscore the modulatory impact of emotional stimuli on cognitive processes affecting oculomotor control.

7.5LGSep 20, 2021Code
Deep Quantile Regression for Uncertainty Estimation in Unsupervised and Supervised Lesion Detection

Haleh Akrami, Anand Joshi, Sergul Aydore et al.

Despite impressive state-of-the-art performance on a wide variety of machine learning tasks, deep learning methods can produce over-confident predictions, particularly with limited training data. Therefore, quantifying uncertainty is particularly important in critical applications such as lesion detection and clinical diagnosis, where a realistic assessment of uncertainty is essential in determining surgical margins, disease status and appropriate treatment. In this work, we propose a novel approach that uses quantile regression for quantifying aleatoric uncertainty in both supervised and unsupervised lesion detection problems. The resulting confidence intervals can be used for lesion detection and segmentation. In the unsupervised setting, we combine quantile regression with the Variational AutoEncoder (VAE). Here we address the problem of quantifying uncertainty in the images that are reconstructed by the VAE as the basis for principled outlier or lesion detection. The VAE models the output as a conditionally independent Gaussian characterized by its mean and variance. Unfortunately, joint optimization of both mean and variance in the VAE leads to the well-known problem of shrinkage or underestimation of variance. Here we describe an alternative Quantile-Regression VAE (QR-VAE) that avoids this variance shrinkage problem by directly estimating conditional quantiles for the input image. Using the estimated quantiles, we compute the conditional mean and variance for the input image from which we then detect outliers by thresholding at a false-discovery-rate corrected p-value. In the supervised setting, we develop binary quantile regression (BQR) for the supervised lesion segmentation task. We show how BQR can be used to capture uncertainty in lesion boundaries in a manner that characterizes expert disagreement.

1.2SPDec 13, 2020
fMRI-Kernel Regression: A Kernel-based Method for Pointwise Statistical Analysis of rs-fMRI for Population Studies

Anand A. Joshi, Soyoung Choi, Haleh Akrami et al.

Due to the spontaneous nature of resting-state fMRI (rs-fMRI) signals, cross-subject comparison and therefore, group studies of rs-fMRI are challenging. Most existing group comparison methods use features extracted from the fMRI time series, such as connectivity features, independent component analysis (ICA), and functional connectivity density (FCD) methods. However, in group studies, especially in the case of spectrum disorders, distances to a single atlas or a representative subject do not fully reflect the differences between subjects that may lie on a multi-dimensional spectrum. Moreover, there may not exist an individual subject or even an average atlas in such cases that is representative of all subjects. Here we describe an approach that measures pairwise distances between the synchronized rs-fMRI signals of pairs of subjects instead of to a single reference point. We also present a method for fMRI data comparison that leverages this generated pairwise feature to establish a radial basis function kernel matrix. This kernel matrix is used in turn to perform kernel regression of rs-fMRI to a clinical variable such as a cognitive or neurophysiological performance score of interest. This method opens a new pointwise analysis paradigm for fMRI data. We demonstrate the application of this method by performing a pointwise analysis on the cortical surface using rs-fMRI data to identify cortical regions associated with variability in ADHD index. While pointwise analysis methods are common in anatomical studies such as cortical thickness analysis and voxel- and tensor-based morphometry and its variants, such a method is lacking for rs-fMRI and could improve the utility of rs-fMRI for group studies. The method presented in this paper is aimed at filling this gap.

3.3LGOct 18, 2020
Addressing Variance Shrinkage in Variational Autoencoders using Quantile Regression

Haleh Akrami, Anand A. Joshi, Sergul Aydore et al.

Estimation of uncertainty in deep learning models is of vital importance, especially in medical imaging, where reliance on inference without taking into account uncertainty could lead to misdiagnosis. Recently, the probabilistic Variational AutoEncoder (VAE) has become a popular model for anomaly detection in applications such as lesion detection in medical images. The VAE is a generative graphical model that is used to learn the data distribution from samples and then generate new samples from this distribution. By training on normal samples, the VAE can be used to detect inputs that deviate from this learned distribution. The VAE models the output as a conditionally independent Gaussian characterized by means and variances for each output dimension. VAEs can therefore use reconstruction probability instead of reconstruction error for anomaly detection. Unfortunately, joint optimization of both mean and variance in the VAE leads to the well-known problem of shrinkage or underestimation of variance. We describe an alternative approach that avoids this variance shrinkage problem by using quantile regression. Using estimated quantiles to compute mean and variance under the Gaussian assumption, we compute reconstruction probability as a principled approach to outlier or anomaly detection. Results on simulated and Fashion MNIST data demonstrate the effectiveness of our approach. We also show how our approach can be used for principled heterogeneous thresholding for lesion detection in brain images.

10.1LGJun 15, 2020
Robust Variational Autoencoder for Tabular Data with Beta Divergence

Haleh Akrami, Sergul Aydore, Richard M. Leahy et al.

We propose a robust variational autoencoder with $β$ divergence for tabular data (RTVAE) with mixed categorical and continuous features. Variational autoencoders (VAE) and their variations are popular frameworks for anomaly detection problems. The primary assumption is that we can learn representations for normal patterns via VAEs and any deviation from that can indicate anomalies. However, the training data itself can contain outliers. The source of outliers in training data include the data collection process itself (random noise) or a malicious attacker (data poisoning) who may target to degrade the performance of the machine learning model. In either case, these outliers can disproportionately affect the training process of VAEs and may lead to wrong conclusions about what the normal behavior is. In this work, we derive a novel form of a variational autoencoder for tabular data sets with categorical and continuous features that is robust to outliers in training data. Our results on the anomaly detection application for network traffic datasets demonstrate the effectiveness of our approach.

9.9MLMay 23, 2019
Robust Variational Autoencoder

Haleh Akrami, Anand A. Joshi, Jian Li et al.

Machine learning methods often need a large amount of labeled training data. Since the training data is assumed to be the ground truth, outliers can severely degrade learned representations and performance of trained models. Here we apply concepts from robust statistics to derive a novel variational autoencoder that is robust to outliers in the training data. Variational autoencoders (VAEs) extract a lower-dimensional encoded feature representation from which we can generate new data samples. Robustness of autoencoders to outliers is critical for generating a reliable representation of particular data types in the encoded space when using corrupted training data. Our robust VAE is based on beta-divergence rather than the standard Kullback-Leibler (KL) divergence. Our proposed lower bound lead to a RVAE model that has the same computational complexity as the VAE and contains a single tuning parameter to control the degree of robustness. We demonstrate the performance of our $β$-divergence based autoencoder for a range of image datasets, showing improved robustness to outliers both qualitatively and quantitatively. We also illustrate the use of our robust VAE for outlier detection.