Equivariance Allows Handling Multiple Nuisance Variables When Analyzing Pooled Neuroimaging Datasets

Pooling multiple neuroimaging datasets across institutions often enables improvements in statistical power when evaluating associations (e.g., between risk factors and disease outcomes) that may otherwise be too weak to detect. When there is only a {\em single} source of variability (e.g., different scanners), domain adaptation and matching the distributions of representations may suffice in many scenarios. But in the presence of {\em more than one} nuisance variable which concurrently influence the measurements, pooling datasets poses unique challenges, e.g., variations in the data can come from both the acquisition method as well as the demographics of participants (gender, age). Invariant representation learning, by itself, is ill-suited to fully model the data generation process. In this paper, we show how bringing recent results on equivariant representation learning (for studying symmetries in neural networks) instantiated on structured spaces together with simple use of classical results on causal inference provides an effective practical solution. In particular, we demonstrate how our model allows dealing with more than one nuisance variable under some assumptions and can enable analysis of pooled scientific datasets in scenarios that would otherwise entail removing a large portion of the samples.

Graph Reparameterizations for Enabling 1000+ Monte Carlo Iterations in Bayesian Deep Neural Networks

Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations may not be sufficient. However, moving to other distributions necessitates Monte Carlo (MC) sampling to estimate quantities such as the KL divergence: it could be expensive and scales poorly as the dimensions of both the input data and the model grow. This is directly related to the structure of the computation graph, which can grow linearly as a function of the number of MC samples needed. Here, we construct a framework to describe these computation graphs, and identify probability families where the graph size can be independent or only weakly dependent on the number of MC samples. These families correspond directly to large classes of distributions. Empirically, we can run a much larger number of iterations for MC approximations for larger architectures used in computer vision with gains in performance measured in confident accuracy, stability of training, memory and training time.

Mixed Effects Neural ODE: A Variational Approximation for Analyzing the Dynamics of Panel Data

Panel data involving longitudinal measurements of the same set of participants taken over multiple time points is common in studies to understand childhood development and disease modeling. Deep hybrid models that marry the predictive power of neural networks with physical simulators such as differential equations, are starting to drive advances in such applications. The task of modeling not just the observations but the hidden dynamics that are captured by the measurements poses interesting statistical/computational questions. We propose a probabilistic model called ME-NODE to incorporate (fixed + random) mixed effects for analyzing such panel data. We show that our model can be derived using smooth approximations of SDEs provided by the Wong-Zakai theorem. We then derive Evidence Based Lower Bounds for ME-NODE, and develop (efficient) training algorithms using MC based sampling methods and numerical ODE solvers. We demonstrate ME-NODE's utility on tasks spanning the spectrum from simulations and toy data to real longitudinal 3D imaging data from an Alzheimer's disease (AD) study, and study its performance in terms of accuracy of reconstruction for interpolation, uncertainty estimates and personalized prediction.

Forward Operator Estimation in Generative Models with Kernel Transfer Operators

Generative models which use explicit density modeling (e.g., variational autoencoders, flow-based generative models) involve finding a mapping from a known distribution, e.g. Gaussian, to the unknown input distribution. This often requires searching over a class of non-linear functions (e.g., representable by a deep neural network). While effective in practice, the associated runtime/memory costs can increase rapidly, usually as a function of the performance desired in an application. We propose a much cheaper (and simpler) strategy to estimate this mapping based on adapting known results in kernel transfer operators. We show that our formulation enables highly efficient distribution approximation and sampling, and offers surprisingly good empirical performance that compares favorably with powerful baselines, but with significant runtime savings. We show that the algorithm also performs well in small sample size settings (in brain imaging).

You Only Sample (Almost) Once: Linear Cost Self-Attention Via Bernoulli Sampling

Transformer-based models are widely used in natural language processing (NLP). Central to the transformer model is the self-attention mechanism, which captures the interactions of token pairs in the input sequences and depends quadratically on the sequence length. Training such models on longer sequences is expensive. In this paper, we show that a Bernoulli sampling attention mechanism based on Locality Sensitive Hashing (LSH), decreases the quadratic complexity of such models to linear. We bypass the quadratic cost by considering self-attention as a sum of individual tokens associated with Bernoulli random variables that can, in principle, be sampled at once by a single hash (although in practice, this number may be a small constant). This leads to an efficient sampling scheme to estimate self-attention which relies on specific modifications of LSH (to enable deployment on GPU architectures). We evaluate our algorithm on the GLUE benchmark with standard 512 sequence length where we see favorable performance relative to a standard pretrained Transformer. On the Long Range Arena (LRA) benchmark, for evaluating performance on long sequences, our method achieves results consistent with softmax self-attention but with sizable speed-ups and memory savings and often outperforms other efficient self-attention methods. Our code is available at https://github.com/mlpen/YOSO

Neural TMDlayer: Modeling Instantaneous flow of features via SDE Generators

We study how stochastic differential equation (SDE) based ideas can inspire new modifications to existing algorithms for a set of problems in computer vision. Loosely speaking, our formulation is related to both explicit and implicit strategies for data augmentation and group equivariance, but is derived from new results in the SDE literature on estimating infinitesimal generators of a class of stochastic processes. If and when there is nominal agreement between the needs of an application/task and the inherent properties and behavior of the types of processes that we can efficiently handle, we obtain a very simple and efficient plug-in layer that can be incorporated within any existing network architecture, with minimal modification and only a few additional parameters. We show promising experiments on a number of vision tasks including few shot learning, point cloud transformers and deep variational segmentation obtaining efficiency or performance improvements.

An Online Riemannian PCA for Stochastic Canonical Correlation Analysis

We present an efficient stochastic algorithm (RSG+) for canonical correlation analysis (CCA) using a reparametrization of the projection matrices. We show how this reparametrization (into structured matrices), simple in hindsight, directly presents an opportunity to repurpose/adjust mature techniques for numerical optimization on Riemannian manifolds. Our developments nicely complement existing methods for this problem which either require $O(d^3)$ time complexity per iteration with $O(\frac{1}{\sqrt{t}})$ convergence rate (where $d$ is the dimensionality) or only extract the top $1$ component with $O(\frac{1}{t})$ convergence rate. In contrast, our algorithm offers a strict improvement for this classical problem: it achieves $O(d^2k)$ runtime complexity per iteration for extracting the top $k$ canonical components with $O(\frac{1}{t})$ convergence rate. While the paper primarily focuses on the formulation and technical analysis of its properties, our experiments show that the empirical behavior on common datasets is quite promising. We also explore a potential application in training fair models where the label of protected attribute is missing or otherwise unavailable.

Connecting What to Say With Where to Look by Modeling Human Attention Traces

We introduce a unified framework to jointly model images, text, and human attention traces. Our work is built on top of the recent Localized Narratives annotation framework [30], where each word of a given caption is paired with a mouse trace segment. We propose two novel tasks: (1) predict a trace given an image and caption (i.e., visual grounding), and (2) predict a caption and a trace given only an image. Learning the grounding of each word is challenging, due to noise in the human-provided traces and the presence of words that cannot be meaningfully visually grounded. We present a novel model architecture that is jointly trained on dual tasks (controlled trace generation and controlled caption generation). To evaluate the quality of the generated traces, we propose a local bipartite matching (LBM) distance metric which allows the comparison of two traces of different lengths. Extensive experiments show our model is robust to the imperfect training data and outperforms the baselines by a clear margin. Moreover, we demonstrate that our model pre-trained on the proposed tasks can be also beneficial to the downstream task of COCO's guided image captioning. Our code and project page are publicly available.

Simpler Certified Radius Maximization by Propagating Covariances

One strategy for adversarially training a robust model is to maximize its certified radius -- the neighborhood around a given training sample for which the model's prediction remains unchanged. The scheme typically involves analyzing a "smoothed" classifier where one estimates the prediction corresponding to Gaussian samples in the neighborhood of each sample in the mini-batch, accomplished in practice by Monte Carlo sampling. In this paper, we investigate the hypothesis that this sampling bottleneck can potentially be mitigated by identifying ways to directly propagate the covariance matrix of the smoothed distribution through the network. To this end, we find that other than certain adjustments to the network, propagating the covariances must also be accompanied by additional accounting that keeps track of how the distributional moments transform and interact at each stage in the network. We show how satisfying these criteria yields an algorithm for maximizing the certified radius on datasets including Cifar-10, ImageNet, and Places365 while offering runtime savings on networks with moderate depth, with a small compromise in overall accuracy. We describe the details of the key modifications that enable practical use. Via various experiments, we evaluate when our simplifications are sensible, and what the key benefits and limitations are.

Nyströmformer: A Nyström-Based Algorithm for Approximating Self-Attention

Transformers have emerged as a powerful tool for a broad range of natural language processing tasks. A key component that drives the impressive performance of Transformers is the self-attention mechanism that encodes the influence or dependence of other tokens on each specific token. While beneficial, the quadratic complexity of self-attention on the input sequence length has limited its application to longer sequences -- a topic being actively studied in the community. To address this limitation, we propose Nystr\"{o}mformer -- a model that exhibits favorable scalability as a function of sequence length. Our idea is based on adapting the Nystr\"{o}m method to approximate standard self-attention with $O(n)$ complexity. The scalability of Nystr\"{o}mformer enables application to longer sequences with thousands of tokens. We perform evaluations on multiple downstream tasks on the GLUE benchmark and IMDB reviews with standard sequence length, and find that our Nystr\"{o}mformer performs comparably, or in a few cases, even slightly better, than standard self-attention. On longer sequence tasks in the Long Range Arena (LRA) benchmark, Nystr\"{o}mformer performs favorably relative to other efficient self-attention methods. Our code is available at https://github.com/mlpen/Nystromformer.