Asymmetric Synthesis of α-Arylcyclohexenones Catalyzed by Diphenylprolinol Silyl Ether.

A general methodology for the asymmetric synthesis of α-arylcyclohexeneones from arylacetones and α,ß-unsaturated aldehydes catalyzed by diphenylprolinol silyl ether followed by p-TSA-mediated cyclization is developed. A variety of arylacetones and α,ß-unsaturated aldehydes were successfully converted to α-arylcyclohexeneones in 34-67% yield, 10:1-100:0 dr, and 81-99% ee. The scalability of this methodology by a gram-scale synthesis and their utility by converting the product to the corresponding epoxide, alcohol, and diol are demonstrated.

LOCALIZING DIFFERENTIALLY EVOLVING COVARIANCE STRUCTURES VIA SCAN STATISTICS.

Recent results in coupled or temporal graphical models offer schemes for estimating the relationship structure between features when the data come from related (but distinct) longitudinal sources. A novel application of these ideas is for analyzing group-level differences, i.e., in identifying if trends of estimated objects (e.g., covariance or precision matrices) are different across disparate conditions (e.g., gender or disease). Often, poor effect sizes make detecting the differential signal over the full set of features difficult: for example, dependencies between only a subset of features may manifest differently across groups. In this work, we first give a parametric model for estimating trends in the space of SPD matrices as a function of one or more covariates. We then generalize scan statistics to graph structures, to search over distinct subsets of features (graph partitions) whose temporal dependency structure may show statistically significant group-wise differences. We theoretically analyze the Family Wise Error Rate (FWER) and bounds on Type 1 and Type 2 error. Evaluating on US census data, we identify groups of states with cultural and legal overlap related to baby name trends and drug usage. On a cohort of individuals with risk factors for Alzheimer's disease (but otherwise cognitively healthy), we find scientifically interesting group differences where the default analysis, i.e., models estimated on the full graph, do not survive reasonable significance thresholds.

Deep Unlearning via Randomized Conditionally Independent Hessians.

Recent legislation has led to interest in machine unlearning, i.e., removing specific training samples from a predictive model as if they never existed in the training dataset. Unlearning may also be required due to corrupted/adversarial data or simply a user's updated privacy requirement. For models which require no training (k-NN), simply deleting the closest original sample can be effective. But this idea is inapplicable to models which learn richer representations. Recent ideas leveraging optimization-based updates scale poorly with the model dimension d, due to inverting the Hessian of the loss function. We use a variant of a new conditional independence coefficient, L-CODEC, to identify a subset of the model parameters with the most semantic overlap on an individual sample level. Our approach completely avoids the need to invert a (possibly) huge matrix. By utilizing a Markov blanket selection, we premise that L-CODEC is also suitable for deep unlearning, as well as other applications in vision. Compared to alternatives, L-CODEC makes approximate unlearning possible in settings that would otherwise be infeasible, including vision models used for face recognition, person re-identification and NLP models that may require unlearning samples identified for exclusion. Code is available at https://github.com/vsingh-group/LCODEC-deep-unlearning.

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 [Farquhar et al., 2020] 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.

Scaling Recurrent Models via Orthogonal Approximations in Tensor Trains.

Modern deep networks have proven to be very effective for analyzing real world images. However, their application in medical imaging is still in its early stages, primarily due to the large size of three-dimensional images, requiring enormous convolutional or fully connected layers - if we treat an image (and not image patches) as a sample. These issues only compound when the focus moves towards longitudinal analysis of 3D image volumes through recurrent structures, and when a point estimate of model parameters is insufficient in scientific applications where a reliability measure is necessary. Using insights from differential geometry, we adapt the tensor train decomposition to construct networks with significantly fewer parameters, allowing us to train powerful recurrent networks on whole brain image volume sequences. We describe the "orthogonal" tensor train, and demonstrate its ability to express a standard network layer both theoretically and empirically. We show its ability to effectively reconstruct whole brain volumes with faster convergence and stronger confidence intervals compared to the standard tensor train decomposition. We provide code and show experiments on the ADNI dataset using image sequences to regress on a cognition related outcome.

Sampling-free Uncertainty Estimation in Gated Recurrent Units with Applications to Normative Modeling in Neuroimaging.

There has recently been a concerted effort to derive mechanisms in vision and machine learning systems to offer uncertainty estimates of the predictions they make. Clearly, there are benefits to a system that is not only accurate but also has a sense for when it is not. Existing proposals center around Bayesian interpretations of modern deep architectures - these are effective but can often be computationally demanding. We show how classical ideas in the literature on exponential families on probabilistic networks provide an excellent starting point to derive uncertainty estimates in Gated Recurrent Units (GRU). Our proposal directly quantifies uncertainty deterministically, without the need for costly sampling-based estimation. We show that while uncertainty is quite useful by itself in computer vision and machine learning, we also demonstrate that it can play a key role in enabling statistical analysis with deep networks in neuroimaging studies with normative modeling methods. To our knowledge, this is the first result describing sampling-free uncertainty estimation for powerful sequential models such as GRUs.

On Training Deep 3D CNN Models with Dependent Samples in Neuroimaging.

There is much interest in developing algorithms based on 3D convolutional neural networks (CNNs) for performing regression and classification with brain imaging data and more generally, with biomedical imaging data. A standard assumption in learning is that the training samples are independently drawn from the underlying distribution. In computer vision, where we have millions of training examples, this assumption is violated but the empirical performance may remain satisfactory. But in many biomedical studies with just a few hundred training examples, one often has multiple samples per participant and/or data may be curated by pooling datasets from a few different institutions. Here, the violation of the independent samples assumption turns out to be more significant, especially in small-to-medium sized datasets. Motivated by this need, we show how 3D CNNs can be modified to deal with dependent samples. We show that even with standard 3D CNNs, there is value in augmenting the network to exploit information regarding dependent samples. We present empirical results for predicting cognitive trajectories (slope and intercept) from morphometric change images derived from multiple time points. With terms which encode dependency between samples in the model, we get consistent improvements over a strong baseline which ignores such knowledge.

DUAL-GLOW: Conditional Flow-Based Generative Model for Modality Transfer.

Positron emission tomography (PET) imaging is an imaging modality for diagnosing a number of neurological diseases. In contrast to Magnetic Resonance Imaging (MRI), PET is costly and involves injecting a radioactive substance into the patient. Motivated by developments in modality transfer in vision, we study the generation of certain types of PET images from MRI data. We derive new flow-based generative models which we show perform well in this small sample size regime (much smaller than dataset sizes available in standard vision tasks). Our formulation, DUAL-GLOW, is based on two invertible networks and a relation network that maps the latent spaces to each other. We discuss how given the prior distribution, learning the conditional distribution of PET given the MRI image reduces to obtaining the conditional distribution between the two latent codes w.r.t. the two image types. We also extend our framework to leverage "side" information (or attributes) when available. By controlling the PET generation through "conditioning" on age, our model is also able to capture brain FDG-PET (hypometabolism) changes, as a function of age. We present experiments on the Alzheimers Disease Neuroimaging Initiative (ADNI) dataset with 826 subjects, and obtain good performance in PET image synthesis, qualitatively and quantitatively better than recent works.