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The detection and estimation of sinusoids is a fundamental signal processing task for many applications related to sensing and communications. While algorithms have been proposed for this setting, quantization is a critical, but often ignored modeling effect. In wireless communications, estimation with low resolution data converters is relevant for reduced power consumption in wideband receivers. Similarly, low resolution sampling in imaging and spectrum sensing allows for efficient data collection. In this work, we propose SignalNet, a neural network architecture that detects the number of sinusoids and estimates their parameters from quantized in-phase and quadrature samples. We incorporate signal reconstruction internally as domain knowledge within the network to enhance learning and surpass traditional algorithms in mean squared error and Chamfer error. We introduce a worst-case learning threshold for comparing the results of our network relative to the underlying data distributions. This threshold provides insight into why neural networks tend to outperform traditional methods and into the learned relationships between the input and output distributions. In simulation, we find that our algorithm is always able to surpass the threshold for three-bit data but often cannot exceed the threshold for one-bit data. We use the learning threshold to explain, in the one-bit case, how our estimators learn to minimize the distributional loss, rather than learn features from the data.

High-order implicit shock tracking is a new class of numerical methods to approximate solutions of conservation laws with non-smooth features. These methods align elements of the computational mesh with non-smooth features to represent them perfectly, allowing high-order basis functions to approximate smooth regions of the solution without the need for nonlinear stabilization, which leads to accurate approximations on traditionally coarse meshes. The hallmark of these methods is the underlying optimization formulation whose solution is a feature-aligned mesh and the corresponding high-order approximation to the flow; the key challenge is robustly solving the central optimization problem. In this work, we develop a robust optimization solver for high-order implicit shock tracking methods so they can be reliably used to simulate complex, high-speed, compressible flows in multiple dimensions. The proposed method integrates practical robustness measures into a sequential quadratic programming method, including dimension- and order-independent simplex element collapses, mesh smoothing, and element-wise solution re-initialization, which prove to be necessary to reliably track complex discontinuity surfaces, such as curved and reflecting shocks, shock formation, and shock-shock interaction. A series of nine numerical experiments -- including two- and three-dimensional compressible flows with complex discontinuity surfaces -- are used to demonstrate: 1) the robustness of the solver, 2) the meshes produced are high-quality and track continuous, non-smooth features in addition to discontinuities, 3) the method achieves the optimal convergence rate of the underlying discretization even for flows containing discontinuities, and 4) the method produces highly accurate solutions on extremely coarse meshes relative to approaches based on shock capturing.

The COVID-19 pandemic has emphasized the need for a robust understanding of epidemic models. Current models of epidemics are classified as either mechanistic or non-mechanistic: mechanistic models make explicit assumptions on the dynamics of disease, whereas non-mechanistic models make assumptions on the form of observed time series. Here, we introduce a simple mixture-based model which bridges the two approaches while retaining benefits of both. The model represents time series of cases and fatalities as a mixture of Gaussian curves, providing a flexible function class to learn from data compared to traditional mechanistic models. Although the model is non-mechanistic, we show that it arises as the natural outcome of a stochastic process based on a networked SIR framework. This allows learned parameters to take on a more meaningful interpretation compared to similar non-mechanistic models, and we validate the interpretations using auxiliary mobility data collected during the COVID-19 pandemic. We provide a simple learning algorithm to identify model parameters and establish theoretical results which show the model can be efficiently learned from data. Empirically, we find the model to have low prediction error. The model is available live at covidpredictions.mit.edu. Ultimately, this allows us to systematically understand the impacts of interventions on COVID-19, which is critical in developing data-driven solutions to controlling epidemics.

High dynamic range (HDR) imaging is of fundamental importance in modern digital photography pipelines and used to produce a high-quality photograph with well exposed regions despite varying illumination across the image. This is typically achieved by merging multiple low dynamic range (LDR) images taken at different exposures. However, over-exposed regions and misalignment errors due to poorly compensated motion result in artefacts such as ghosting. In this paper, we present a new HDR imaging technique that specifically models alignment and exposure uncertainties to produce high quality HDR results. We introduce a strategy that learns to jointly align and assess the alignment and exposure reliability using an HDR-aware, uncertainty-driven attention map that robustly merges the frames into a single high quality HDR image. Further, we introduce a progressive, multi-stage image fusion approach that can flexibly merge any number of LDR images in a permutation-invariant manner. Experimental results show our method can produce better quality HDR images with up to 0.8dB PSNR improvement to the state-of-the-art, and subjective improvements in terms of better detail, colours, and fewer artefacts.

Policy gradient (PG) methods are popular reinforcement learning (RL) methods where a baseline is often applied to reduce the variance of gradient estimates. In multi-agent RL (MARL), although the PG theorem can be naturally extended, the effectiveness of multi-agent PG (MAPG) methods degrades as the variance of gradient estimates increases rapidly with the number of agents. In this paper, we offer a rigorous analysis of MAPG methods by, firstly, quantifying the contributions of the number of agents and agents' explorations to the variance of MAPG estimators. Based on this analysis, we derive the optimal baseline (OB) that achieves the minimal variance. In comparison to the OB, we measure the excess variance of existing MARL algorithms such as vanilla MAPG and COMA. Considering using deep neural networks, we also propose a surrogate version of OB, which can be seamlessly plugged into any existing PG methods in MARL. On benchmarks of Multi-Agent MuJoCo and StarCraft challenges, our OB technique effectively stabilises training and improves the performance of multi-agent PPO and COMA algorithms by a significant margin.

Heatmap-based methods dominate in the field of human pose estimation by modelling the output distribution through likelihood heatmaps. In contrast, regression-based methods are more efficient but suffer from inferior performance. In this work, we explore maximum likelihood estimation (MLE) to develop an efficient and effective regression-based methods. From the perspective of MLE, adopting different regression losses is making different assumptions about the output density function. A density function closer to the true distribution leads to a better regression performance. In light of this, we propose a novel regression paradigm with Residual Log-likelihood Estimation (RLE) to capture the underlying output distribution. Concretely, RLE learns the change of the distribution instead of the unreferenced underlying distribution to facilitate the training process. With the proposed reparameterization design, our method is compatible with off-the-shelf flow models. The proposed method is effective, efficient and flexible. We show its potential in various human pose estimation tasks with comprehensive experiments. Compared to the conventional regression paradigm, regression with RLE bring 12.4 mAP improvement on MSCOCO without any test-time overhead. Moreover, for the first time, especially on multi-person pose estimation, our regression method is superior to the heatmap-based methods. Our code is available at //github.com/Jeff-sjtu/res-loglikelihood-regression

Implicit probabilistic models are models defined naturally in terms of a sampling procedure and often induces a likelihood function that cannot be expressed explicitly. We develop a simple method for estimating parameters in implicit models that does not require knowledge of the form of the likelihood function or any derived quantities, but can be shown to be equivalent to maximizing likelihood under some conditions. Our result holds in the non-asymptotic parametric setting, where both the capacity of the model and the number of data examples are finite. We also demonstrate encouraging experimental results.

The Normalized Cut (NCut) objective function, widely used in data clustering and image segmentation, quantifies the cost of graph partitioning in a way that biases clusters or segments that are balanced towards having lower values than unbalanced partitionings. However, this bias is so strong that it avoids any singleton partitions, even when vertices are very weakly connected to the rest of the graph. Motivated by the B\"uhler-Hein family of balanced cut costs, we propose the family of Compassionately Conservative Balanced (CCB) Cut costs, which are indexed by a parameter that can be used to strike a compromise between the desire to avoid too many singleton partitions and the notion that all partitions should be balanced. We show that CCB-Cut minimization can be relaxed into an orthogonally constrained $\ell_{\tau}$-minimization problem that coincides with the problem of computing Piecewise Flat Embeddings (PFE) for one particular index value, and we present an algorithm for solving the relaxed problem by iteratively minimizing a sequence of reweighted Rayleigh quotients (IRRQ). Using images from the BSDS500 database, we show that image segmentation based on CCB-Cut minimization provides better accuracy with respect to ground truth and greater variability in region size than NCut-based image segmentation.

We explore deep reinforcement learning methods for multi-agent domains. We begin by analyzing the difficulty of traditional algorithms in the multi-agent case: Q-learning is challenged by an inherent non-stationarity of the environment, while policy gradient suffers from a variance that increases as the number of agents grows. We then present an adaptation of actor-critic methods that considers action policies of other agents and is able to successfully learn policies that require complex multi-agent coordination. Additionally, we introduce a training regimen utilizing an ensemble of policies for each agent that leads to more robust multi-agent policies. We show the strength of our approach compared to existing methods in cooperative as well as competitive scenarios, where agent populations are able to discover various physical and informational coordination strategies.