The Moran process is a classic stochastic process that models invasion dynamics on graphs. A single "mutant" (e.g., a new opinion, strain, social trait etc.) invades a population of residents spread over the nodes of a graph. The mutant fitness advantage $\delta\geq 0$ determines how aggressively mutants propagate to their neighbors. The quantity of interest is the fixation probability, i.e., the probability that the initial mutant eventually takes over the whole population. However, in realistic settings, the invading mutant has an advantage only in certain locations. E.g., a bacterial mutation allowing for lactose metabolism only confers an advantage on places where dairy products are present. In this paper we introduce the positional Moran process, a natural generalization in which the mutant fitness advantage is only realized on specific nodes called active nodes. The associated optimization problem is fixation maximization: given a budget $k$, choose a set of $k$ active nodes that maximize the fixation probability of the invading mutant. We show that the problem is NP-hard, while the optimization function is not submodular, thus indicating strong computational hardness. Then we focus on two natural limits. In the limit of $\delta\to\infty$ (strong selection), although the problem remains NP-hard, the optimization function becomes submodular and thus admits a constant-factor approximation using a simple greedy algorithm. In the limit of $\delta\to 0$ (weak selection), we show that in $O(m^\omega)$ time we can obtain a tight approximation, where $m$ is the number of edges and $\omega$ is the matrix-multiplication exponent. Finally, we present an experimental evaluation of the new algorithms together with some proposed heuristics.
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Processing 是一門開源編程語言和與之配套的集成開發環境（IDE）的名稱。Processing 在電子藝術和視覺設計社區被用來教授編程基礎，并運用于大量的新媒體和互動藝術作品中。
The reinforcement learning (RL) problem is rife with sources of non-stationarity, making it a notoriously difficult problem domain for the application of neural networks. We identify a mechanism by which non-stationary prediction targets can prevent learning progress in deep RL agents: \textit{capacity loss}, whereby networks trained on a sequence of target values lose their ability to quickly update their predictions over time. We demonstrate that capacity loss occurs in a range of RL agents and environments, and is particularly damaging to performance in sparse-reward tasks. We then present a simple regularizer, Initial Feature Regularization (InFeR), that mitigates this phenomenon by regressing a subspace of features towards its value at initialization, leading to significant performance improvements in sparse-reward environments such as Montezuma's Revenge. We conclude that preventing capacity loss is crucial to enable agents to maximally benefit from the learning signals they obtain throughout the entire training trajectory.
Unsupervised domain adaptation approaches have recently succeeded in various medical image segmentation tasks. The reported works often tackle the domain shift problem by aligning the domain-invariant features and minimizing the domain-specific discrepancies. That strategy works well when the difference between a specific domain and between different domains is slight. However, the generalization ability of these models on diverse imaging modalities remains a significant challenge. This paper introduces UDA-VAE++, an unsupervised domain adaptation framework for cardiac segmentation with a compact loss function lower bound. To estimate this new lower bound, we develop a novel Structure Mutual Information Estimation (SMIE) block with a global estimator, a local estimator, and a prior information matching estimator to maximize the mutual information between the reconstruction and segmentation tasks. Specifically, we design a novel sequential reparameterization scheme that enables information flow and variance correction from the low-resolution latent space to the high-resolution latent space. Comprehensive experiments on benchmark cardiac segmentation datasets demonstrate that our model outperforms previous state-of-the-art qualitatively and quantitatively. The code is available at //github.com/LOUEY233/Toward-Mutual-Information}{//github.com/LOUEY233/Toward-Mutual-Information
Interacting agents receive public information at no cost and flexibly acquire private information at a cost proportional to entropy reduction. When a policymaker provides more public information, agents acquire less private information, thus lowering information costs. Does more public information raise or reduce uncertainty faced by agents? Is it beneficial or detrimental to welfare? To address these questions, we examine the impacts of public information on flexible information acquisition in a linear-quadratic-Gaussian game with arbitrary quadratic material welfare. More public information raises uncertainty if and only if the game exhibits strategic complementarity, which can be harmful to welfare. However, when agents acquire a large amount of information, more provision of public information increases welfare through a substantial reduction in the cost of information. We give a necessary and sufficient condition for welfare to increase with public information and identify optimal public information disclosure, which is either full or partial disclosure depending upon the welfare function and the slope of the best response.
Bayesian optimization is a popular method for optimizing expensive black-box functions. Yet it oftentimes struggles in high dimensions where the computation could be prohibitively heavy. To alleviate this problem, we introduce Coordinate backoff Bayesian Optimization (CobBO) with two-stage kernels. During each round, the first stage uses a simple coarse kernel that sacrifices the approximation accuracy for computational efficiency. It captures the global landscape by purposely smoothing away local fluctuations. Then, in the second stage of the same round, past observed points in the full space are projected to the selected subspace to form virtual points. These virtual points, along with the means and variances of their unknown function values estimated using the simple kernel of the first stage, are fitted to a more sophisticated kernel model in the second stage. Within the selected low dimensional subspace, the computational cost of conducting Bayesian optimization therein becomes affordable. To further enhance the performance, a sequence of consecutive observations in the same subspace are collected, which can effectively refine the approximation of the function. This refinement lasts until a stopping rule is met determining when to back off from a certain subspace and switch to another. This decoupling significantly reduces the computational burden in high dimensions, which fully leverages the observations in the whole space rather than only relying on observations in each coordinate subspace. Extensive evaluations show that CobBO finds solutions comparable to or better than other state-of-the-art methods for dimensions ranging from tens to hundreds, while reducing both the trial complexity and computational costs.
The adoption of Unmanned Aerial Vehicles (UAVs) for public safety applications has skyrocketed in the last years. Leveraging on Physical Random Access Channel (PRACH) preambles, in this paper we pioneer a novel localization technique for UAVs equipped with cellular base stations used in emergency scenarios. We exploit the new concept of Orthogonal Time Frequency Space (OTFS) modulation (tolerant to channel Doppler spread caused by UAVs motion) to build a fully standards-compliant OTFS-modulated PRACH transmission and reception scheme able to perform time-of-arrival (ToA) measurements. First, we analyze such novel ToA ranging technique, both analytically and numerically, to accurately and iteratively derive the distance between localized users and the points traversed by the UAV along its trajectory. Then, we determine the optimal UAV speed as a trade-off between the accuracy of the ranging technique and the power needed by the UAV to reach and keep its speed during emergency operations. Finally, we demonstrate that our solution outperforms standard PRACH-based localization techniques in terms of Root Mean Square Error (RMSE) by about 20% in quasi-static conditions and up to 80% in high-mobility conditions.
Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates--while accounting for this structured dependence--remains a challenge. We introduce a Bayesian decision analysis for subset selection with LMMs. Using a Mahalanobis loss function that incorporates the structured dependence, we derive optimal linear coefficients for (i) any given subset of variables and (ii) all subsets of variables that satisfy a cardinality constraint. Crucially, these estimates inherit shrinkage or regularization and uncertainty quantification from the underlying Bayesian model, and apply for any well-specified Bayesian LMM. More broadly, our decision analysis strategy deemphasizes the role of a single "best" subset, which is often unstable and limited in its information content, and instead favors a collection of near-optimal subsets. This collection is summarized by key member subsets and variable-specific importance metrics. Customized subset search and out-of-sample approximation algorithms are provided for more scalable computing. These tools are applied to simulated data and a longitudinal physical activity dataset, and demonstrate excellent prediction, estimation, and selection ability.
Computing a maximum independent set (MaxIS) is a fundamental NP-hard problem in graph theory, which has important applications in a wide spectrum of fields. Since graphs in many applications are changing frequently over time, the problem of maintaining a MaxIS over dynamic graphs has attracted increasing attention over the past few years. Due to the intractability of maintaining an exact MaxIS, this paper aims to develop efficient algorithms that can maintain an approximate MaxIS with an accuracy guarantee theoretically. In particular, we propose a framework that maintains a $(\frac{\Delta}{2} + 1)$-approximate MaxIS over dynamic graphs and prove that it achieves a constant approximation ratio in many real-world networks. To the best of our knowledge, this is the first non-trivial approximability result for the dynamic MaxIS problem. Following the framework, we implement an efficient linear-time dynamic algorithm and a more effective dynamic algorithm with near-linear expected time complexity. Our thorough experiments over real and synthetic graphs demonstrate the effectiveness and efficiency of the proposed algorithms, especially when the graph is highly dynamic.
We consider M-estimation problems, where the target value is determined using a minimizer of an expected functional of a Levy process. With discrete observations from the Levy process, we can produce a "quasi-path" by shuffling increments of the Levy process, we call it a quasi-process. Under a suitable sampling scheme, a quasi-process can converge weakly to the true process according to the properties of the stationary and independent increments. Using this resampling technique, we can estimate objective functionals similar to those estimated using the Monte Carlo simulations, and it is available as a contrast function. The M-estimator based on these quasi-processes can be consistent and asymptotically normal.
Interactive segmentation allows users to extract target masks by making positive/negative clicks. Although explored by many previous works, there is still a gap between academic approaches and industrial needs: first, existing models are not efficient enough to work on low power devices; second, they perform poorly when used to refine preexisting masks as they could not avoid destroying the correct part. FocalClick solves both issues at once by predicting and updating the mask in localized areas. For higher efficiency, we decompose the slow prediction on the entire image into two fast inferences on small crops: a coarse segmentation on the Target Crop, and a local refinement on the Focus Crop. To make the model work with preexisting masks, we formulate a sub-task termed Interactive Mask Correction, and propose Progressive Merge as the solution. Progressive Merge exploits morphological information to decide where to preserve and where to update, enabling users to refine any preexisting mask effectively. FocalClick achieves competitive results against SOTA methods with significantly smaller FLOPs. It also shows significant superiority when making corrections on preexisting masks. Code and data will be released at github.com/XavierCHEN34/ClickSEG
We present the Sequential Aggregation and Rematerialization (SAR) scheme for distributed full-batch training of Graph Neural Networks (GNNs) on large graphs. Large-scale training of GNNs has recently been dominated by sampling-based methods and methods based on non-learnable message passing. SAR on the other hand is a distributed technique that can train any GNN type directly on an entire large graph. The key innovation in SAR is the distributed sequential rematerialization scheme which sequentially re-constructs then frees pieces of the prohibitively large GNN computational graph during the backward pass. This results in excellent memory scaling behavior where the memory consumption per worker goes down linearly with the number of workers, even for densely connected graphs. Using SAR, we report the largest applications of full-batch GNN training to-date, and demonstrate large memory savings as the number of workers increases. We also present a general technique based on kernel fusion and attention-matrix rematerialization to optimize both the runtime and memory efficiency of attention-based models. We show that, coupled with SAR, our optimized attention kernels lead to significant speedups and memory savings in attention-based GNNs.We made the SAR GNN training library publicy available: \url{//github.com/IntelLabs/SAR}.
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