We consider multi-draft speculative sampling, where the proposal sequences are sampled independently from different draft models. At each step, a token-level draft selection scheme takes a list of valid tokens as input and produces an output token whose distribution matches that of the target model. Previous works have demonstrated that the optimal scheme (which maximizes the probability of accepting one of the input tokens) can be cast as a solution to a linear program. In this work we show that the optimal scheme can be decomposed into a two-step solution: in the first step an importance sampling (IS) type scheme is used to select one intermediate token; in the second step (single-draft) speculative sampling is applied to generate the output token. For the case of two identical draft models we further 1) establish a necessary and sufficient condition on the distributions of the target and draft models for the acceptance probability to equal one and 2) provide an explicit expression for the optimal acceptance probability. Our theoretical analysis also motives a new class of token-level selection schemes based on weighted importance sampling. Our experimental results demonstrate consistent improvements in the achievable block efficiency and token rates over baseline schemes in a number of scenarios.

Uncertainty quantification is an important prerequisite for the deployment of deep learning models in safety-critical areas. Yet, this hinges on the uncertainty estimates being useful to the extent the prediction intervals are well-calibrated and sharp. In the absence of inherent uncertainty estimates (e.g. pretrained models predicting only point estimates), popular approaches that operate post-hoc include Laplace’s method and split conformal prediction (split-CP). However, Laplace’s method can be miscalibrated when the model is misspecified and split-CP requires sample splitting, and thus comes at the expense of statistical efficiency. In this work, we construct prediction intervals for neural network regressors post-hoc without held-out data. This is achieved by approximating the full conformal prediction method (full-CP). Whilst full-CP nominally requires retraining the model for every test point and candidate label, we propose to train just once and locally perturb model parameters using Gauss-Newton influence to approximate the effect of retraining. Coupled with linearization of the network, we express the absolute residual nonconformity score as a piecewise linear function of the candidate label allowing for an efficient procedure that avoids the exhaustive search over the output space. On standard regression benchmarks and bounding box localization, we show the resulting prediction intervals are locally-adaptive and often tighter than those of split-CP.

Conformal prediction is a distribution-free uncertainty quantification method that has gained popularity in the machine learning community due to its finite-sample guarantees and ease of use. Its most common variant, dubbed split conformal prediction, is also computationally efficient as it boils down to collecting statistics of the model predictions on some calibration data not yet seen by the model. Nonetheless, these guarantees only hold if the calibration and test data are exchangeable, a condition that is difficult to verify and often violated in practice due to so-called distribution shifts. The literature is rife with methods to mitigate the loss in coverage in this non-exchangeable setting, but these methods require some prior information on the type of distribution shift to be expected at test time. In this work, we study this problem via a new perspective, through the lens of optimal transport, and show that it is possible to estimate the loss in coverage and mitigate arbitrary distribution shifts, offering a principled and broadly applicable solution.

The pandemic in 2020 and 2021 had enormous economic and societal consequences, and studies show that contact tracing algorithms can be key in the early containment of the virus. While large strides have been made towards more effective contact tracing algorithms, we argue that privacy concerns currently hold deployment back. The essence of a contact tracing algorithm constitutes the communication of a risk score. Yet, it is precisely the communication and release of this score to a user that an adversary can leverage to gauge the private health status of an individual. We pinpoint a realistic attack scenario and propose a contact tracing algorithm with differential privacy guarantees against this attack. The algorithm is tested on the two most widely used agent-based COVID19 simulators and demonstrates superior performance in a wide range of settings. Especially for realistic test scenarios and while releasing each risk score with epsilon=1 differential privacy, we achieve a two to ten-fold reduction in the infection rate of the virus. To the best of our knowledge, this presents the first contact tracing algorithm with differential privacy guarantees when revealing risk scores for COVID19.

We propose two extensions to existing importance sampling based methods for lossy compression. First, we introduce an importance sampling based compression scheme that is a variant of ordered random coding (Theis and Ahmed, 2022) and is amenable to direct evaluation of the achievable compression rate for a finite number of samples. Our second and major contribution is the \emph{importance matching lemma}, which is a finite proposal counterpart of the recently introduced {Poisson matching lemma} (Li and Anantharam, 2021). By integrating with deep learning, we provide a new coding scheme for distributed lossy compression with side information at the decoder. We demonstrate the effectiveness of the proposed scheme through experiments involving synthetic Gaussian sources, distributed image compression with MNIST and vertical federated learning with CIFAR-10.

We investigate contrastive learning in the federated setting through the lens of Sim- CLR and multi-view mutual information maximization. In doing so, we uncover a connection between contrastive representation learning and user verification; by adding a user verification loss to each client’s local SimCLR loss we recover a lower bound to the global multi-view mutual information. To accommodate for the case of when some labelled data are available at the clients, we extend our SimCLR variant to the federated semi-supervised setting. We see that a supervised SimCLR objective can be obtained with two changes: a) the contrastive loss is computed between datapoints that share the same label and b) we require an additional auxiliary head that predicts the correct labels from either of the two views. Along with the proposed SimCLR extensions, we also study how different sources of non-i.i.d.-ness can impact the performance of federated unsupervised learning through global mutual information maximization; we find that a global objective is beneficial for some sources of non-i.i.d.-ness but can be detrimental for others. We empirically evaluate our proposed extensions in various tasks to validate our claims and furthermore demonstrate that our proposed modifications generalize to other pretraining methods.

Conformal Prediction (CP) is a distribution-free uncertainty estimation framework that constructs prediction sets guaranteed to contain the true answer with a user-specified probability. Intuitively, the size of the prediction set encodes a general notion of uncertainty, with larger sets associated with higher degrees of uncertainty. In this work, we leverage information theory to connect conformal prediction to other notions of uncertainty. More precisely, we prove three different ways to upper bound the intrinsic uncertainty, as described by the conditional entropy of the target variable given the inputs, by combining CP with information theoretical inequalities. Moreover, we demonstrate two direct and useful applications of such connection between conformal prediction and information theory: (i) more principled and effective conformal training objectives that generalize previous approaches and enable end-to-end training of machine learning models from scratch, and (ii) a natural mechanism to incorporate side information into conformal prediction. We empirically validate both applications in centralized and federated learning settings, showing our theoretical results translate to lower inefficiency (average prediction set size) for popular CP methods.

The problem of heterogeneous clients in federated learning has recently drawn a lot of attention. Spectral model sharding, i.e., partitioning the model parameters into low-rank matrices based on the singular value decomposition, has been one of the proposed solutions for more efficient on-device training in such settings. In this work we present two sampling strategies for such sharding, obtained as solutions to specific optimization problems. The first produces unbiased estimators of the original weights, while the second aims to minimize the squared approximation error. We discuss how both of these estimators can be incorporated in the federated learning loop and practical considerations that arise during local training. Empirically, we demonstrate that both of these methods can lead to improved performance in various commonly used datasets.

Pandemics have a major impact on society and the economy. In the case of a new virus, such as COVID-19, high-grade tests and vaccines might be slow to develop and scarce in the crucial initial phase. With no time to waste and lock-downs being expensive, contact tracing is thus an essential tool for policymakers. In theory, statistical inference on a virus transmission model can provide an effective method for tracing infections. However, in practice, such algorithms need to run decentralized, rendering existing methods – that require hundreds or even thousands of daily messages per person – infeasible. In this paper, we develop an algorithm that (i) requires only a few (2-5) daily messages, (ii) works with extremely low bandwidths (3-5 bits) and (iii) enables quarantining and targeted testing that drastically reduces the peak and length of the pandemic. We compare the effectiveness of our algorithm using two agent-based simulators of realistic contact patterns and pandemic parameters and show that it performs well even with low bandwidth, imprecise tests, and incomplete population coverage.

We consider the problem of training User Verification (UV) models in federated setup, where each user has access to the data of only one class and user embeddings cannot be shared with the server or other users. To address this problem, we propose Federated User Verification (FedUV), a framework in which users jointly learn a set of vectors and maximize the correlation of their instance embeddings with a secret linear combination of those vectors. We show that choosing the linear combinations from the codewords of an error-correcting code allows users to collaboratively train the model without revealing their embedding vectors. We present the experimental results for user verification with voice, face, and handwriting data and show that FedUV is on par with existing approaches, while not sharing the embeddings with other users or the server.

When quantizing neural networks, assigning each floating-point weight to its nearest fixed-point value is the predominant approach. We find that, perhaps surprisingly, this is not the best we can do. In this paper, we propose AdaRound, a better weight-rounding mechanism for post-training quantization that adapts to the data and the task loss. AdaRound is fast, does not require fine-tuning of the network, and only uses a small amount of unlabelled data. We start by theoretically analyzing the rounding problem for a pre-trained neural network. By approximating the task loss with a Taylor series expansion, the rounding task is posed as a quadratic unconstrained binary optimization problem. We simplify this to a layer-wise local loss and propose to optimize this loss with a soft relaxation. AdaRound not only outperforms rounding-to-nearest by a significant margin but also establishes a new state-of-the-art for post-training quantization on several networks and tasks. Without fine-tuning, we can quantize the weights of Resnet18 and Resnet50 to 4 bits while staying within an accuracy loss of 1%.

We introduce Bayesian Bits, a practical method for joint mixed precision quantization and pruning through gradient based optimization. Bayesian Bits employs a novel decomposition of the quantization operation, which sequentially considers doubling the bit width. At each new bit width, the residual error between the full precision value and the previously rounded value is quantized. We then decide whether or not to add this quantized residual error for a higher effective bit width and lower quantization noise. By starting with a power-of-two bit width, this decomposition will always produce hardware-friendly configurations, and through an additional 0-bit option, serves as a unified view of pruning and quantization. Bayesian Bits then introduces learnable stochastic gates, which collectively control the bit width of the given tensor. As a result, we can obtain low bit solutions by performing approximate inference over the gates, with prior distributions that encourage most of them to be switched off. We experimentally validate our proposed method on several benchmark datasets and show that we can learn pruned, mixed precision networks that provide a better trade-off between accuracy and efficiency than their static bit width equivalents.

We present a new family of exchangeable stochastic processes, the Functional Neural Processes (FNPs). FNPs model distributions over functions by learning a graph of dependencies on top of latent representations of the points in the given dataset. In doing so, they define a Bayesian model without explicitly positing a prior distribution over latent global parameters; they instead adopt priors over the relational structure of the given dataset, a task that is much simpler. We show how we can learn such models from data, demonstrate that they are scalable to large datasets through mini-batch optimization and describe how we can make predictions for new points via their posterior predictive distribution. We experimentally evaluate FNPs on the tasks of toy regression and image classification and show that, when compared to baselines that employ global latent parameters, they offer both competitive predictions as well as more robust uncertainty estimates.

We reinterpret multiplicative noise in neural networks as auxiliary random variables that augment the approximate posterior in a variational setting for Bayesian neural networks. We show that through this interpretation it is both efficient and straightforward to improve the approximation by employing normalizing flows while still allowing for local reparametrizations and a tractable lower bound. In experiments we show that with this new approximation we can significantly improve upon classical mean field for Bayesian neural networks on both predictive accuracy as well as predictive uncertainty.

Learning individual-level causal effects from observational data, such as inferring the most effective medication for a specific patient, is a problem of growing importance for policy makers. The most important aspect of inferring causal effects from observational data is the handling of confounders, factors that affect both an intervention and its outcome. A carefully designed observational study attempts to measure all important confounders. However, even if one does not have direct access to all confounders, there may exist noisy and uncertain measurement of proxies for confounders. We build on recent advances in latent variable modeling to simultaneously estimate the unknown latent space summarizing the confounders and the causal effect. Our method is based on Variational Autoencoders (VAE) which follow the causal structure of inference with proxies. We show our method is significantly more robust than existing methods, and matches the state-of-the-art on previous benchmarks focused on individual treatment effects.

Compression and computational efficiency in deep learning have become a problem of great significance. In this work, we argue that the most principled and effective way to attack this problem is by adopting a Bayesian point of view, where through sparsity inducing priors we prune large parts of the network. We introduce two novelties in this paper: 1) we use hierarchical priors to prune nodes instead of individual weights, and 2) we use the posterior uncertainties to determine the optimal fixed point precision to encode the weights. Both factors significantly contribute to achieving the state of the art in terms of compression rates, while still staying competitive with methods designed to optimize for speed or energy efficiency.

We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian (Gupta & Nagar ’99) parameter posterior distribution where we explicitly model the covariance among the input and output dimensions of each layer. Furthermore, with approximate covariance matrices we can achieve a more efficient way to represent those correlations that is also cheaper than fully factorized parameter posteriors. We further show that with the “local reprarametrization trick" (Kingma & Welling ’15) on this posterior distribution we arrive at a Gaussian Process (Rasmussen ’06) interpretation of the hidden units in each layer and we, similarly with (Gal & Ghahramani ’15), provide connections with deep Gaussian processes. We continue in taking advantage of this duality and incorporate “pseudo-data” (Snelson & Ghahramani ’05) in our model, which in turn allows for more efficient posterior sampling while maintaining the properties of the original model. The validity of the proposed approach is verified through extensive experiments.