Within the likes of any highly contagious and unpredictable disease, lies a predictable and attainable growth rate that researchers can find in order to make logistical conclusions about that particular disease and its affected regions' counterparts. The foundation that researchers pull from when studying a particular disease and looking for its growth rate is the Susceptible-Infected-Removed (SIR) model, presented by a series of differential equations. The issue with the SIR model lies not in its complexity, but actually its simplicity and lack of a potentially high-finite amount of factors; the limit being bounded by the amount of data available for that particular factor. Our research involves the application of multiple regressions to pinpoint and identify our Covid lockdown periods, followed by the modification of the SIR model. This involved creating new model approximations such as the time-delayed SIR model and the reinfected SIR model in order to take into account factors such as incubation and reinfection, and get the lowest error discrepancy as possible for our infection rate. We were able to conclude that the more factors that we took into account, our error rate became lower and our results became more accurate. We could also identify outlier Metros and draw certain conclusions on performance level and the reasons behind them. We then moved on to find correlations, if any, between the infection rates and outside factors. We looked at demographic and weather data to demonstrate whether correlations appeared. We found that there are a few factors with high correlations, including graduate education and low temperatures.
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Transformers achieve state-of-the-art accuracy and robustness across many tasks, but an understanding of the inductive biases that they have and how those biases are different from other neural network architectures remains elusive. Various neural network architectures such as fully connected networks have been found to have a simplicity bias towards simple functions of the data; one version of this simplicity bias is a spectral bias to learn simple functions in the Fourier space. In this work, we identify the notion of sensitivity of the model to random changes in the input as a notion of simplicity bias which provides a unified metric to explain the simplicity and spectral bias of transformers across different data modalities. We show that transformers have lower sensitivity than alternative architectures, such as LSTMs, MLPs and CNNs, across both vision and language tasks. We also show that low-sensitivity bias correlates with improved robustness; furthermore, it can also be used as an efficient intervention to further improve the robustness of transformers.
We investigate the emergence of periodic behavior in opinion dynamics and its underlying geometry. For this, we use a bounded-confidence model with contrarian agents in a convolution social network. This means that agents adapt their opinions by interacting with their neighbors in a time-varying social network. Being contrarian, the agents are kept from reaching consensus. This is the key feature that allows the emergence of cyclical trends. We show that the systems either converge to nonconsensual equilibrium or are attracted to periodic or quasi-periodic orbits. We bound the dimension of the attractors and the period of cyclical trends. We exhibit instances where each orbit is dense and uniformly distributed within its attractor. We also investigate the case of randomly changing social networks.
The Cheyette model is a quasi-Gaussian volatility interest rate model widely used to price interest rate derivatives such as European and Bermudan Swaptions for which Monte Carlo simulation has become the industry standard. In low dimensions, these approaches provide accurate and robust prices for European Swaptions but, even in this computationally simple setting, they are known to underestimate the value of Bermudan Swaptions when using the state variables as regressors. This is mainly due to the use of a finite number of predetermined basis functions in the regression. Moreover, in high-dimensional settings, these approaches succumb to the Curse of Dimensionality. To address these issues, Deep-learning techniques have been used to solve the backward Stochastic Differential Equation associated with the value process for European and Bermudan Swaptions; however, these methods are constrained by training time and memory. To overcome these limitations, we propose leveraging Tensor Neural Networks as they can provide significant parameter savings while attaining the same accuracy as classical Dense Neural Networks. In this paper we rigorously benchmark the performance of Tensor Neural Networks and Dense Neural Networks for pricing European and Bermudan Swaptions, and we show that Tensor Neural Networks can be trained faster than Dense Neural Networks and provide more accurate and robust prices than their Dense counterparts.
A recent development in Bayesian optimization is the use of local optimization strategies, which can deliver strong empirical performance on high-dimensional problems compared to traditional global strategies. The "folk wisdom" in the literature is that the focus on local optimization sidesteps the curse of dimensionality; however, little is known concretely about the expected behavior or convergence of Bayesian local optimization routines. We first study the behavior of the local approach, and find that the statistics of individual local solutions of Gaussian process sample paths are surprisingly good compared to what we would expect to recover from global methods. We then present the first rigorous analysis of such a Bayesian local optimization algorithm recently proposed by M\"uller et al. (2021), and derive convergence rates in both the noisy and noiseless settings.
We consider the task of estimating a low-rank matrix from non-linear and noisy observations. We prove a strong universality result showing that Bayes-optimal performances are characterized by an equivalent Gaussian model with an effective prior, whose parameters are entirely determined by an expansion of the non-linear function. In particular, we show that to reconstruct the signal accurately, one requires a signal-to-noise ratio growing as $N^{\frac 12 (1-1/k_F)}$, where $k_F$ is the first non-zero Fisher information coefficient of the function. We provide asymptotic characterization for the minimal achievable mean squared error (MMSE) and an approximate message-passing algorithm that reaches the MMSE under conditions analogous to the linear version of the problem. We also provide asymptotic errors achieved by methods such as principal component analysis combined with Bayesian denoising, and compare them with Bayes-optimal MMSE.
VPN adoption has seen steady growth over the past decade due to increased public awareness of privacy and surveillance threats. In response, certain governments are attempting to restrict VPN access by identifying connections using "dual use" DPI technology. To investigate the potential for VPN blocking, we develop mechanisms for accurately fingerprinting connections using OpenVPN, the most popular protocol for commercial VPN services. We identify three fingerprints based on protocol features such as byte pattern, packet size, and server response. Playing the role of an attacker who controls the network, we design a two-phase framework that performs passive fingerprinting and active probing in sequence. We evaluate our framework in partnership with a million-user ISP and find that we identify over 85% of OpenVPN flows with only negligible false positives, suggesting that OpenVPN-based services can be effectively blocked with little collateral damage. Although some commercial VPNs implement countermeasures to avoid detection, our framework successfully identified connections to 34 out of 41 "obfuscated" VPN configurations. We discuss the implications of the VPN fingerprintability for different threat models and propose short-term defenses. In the longer term, we urge commercial VPN providers to be more transparent about their obfuscation approaches and to adopt more principled detection countermeasures, such as those developed in censorship circumvention research.
Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of Artificial General Intelligence (AGI). With the ongoing development of foundation models, e.g., Large Language Models (LLMs), there is a growing interest in exploring their abilities in reasoning tasks. In this paper, we introduce seminal foundation models proposed or adaptable for reasoning, highlighting the latest advancements in various reasoning tasks, methods, and benchmarks. We then delve into the potential future directions behind the emergence of reasoning abilities within foundation models. We also discuss the relevance of multimodal learning, autonomous agents, and super alignment in the context of reasoning. By discussing these future research directions, we hope to inspire researchers in their exploration of this field, stimulate further advancements in reasoning with foundation models, and contribute to the development of AGI.
Understanding causality helps to structure interventions to achieve specific goals and enables predictions under interventions. With the growing importance of learning causal relationships, causal discovery tasks have transitioned from using traditional methods to infer potential causal structures from observational data to the field of pattern recognition involved in deep learning. The rapid accumulation of massive data promotes the emergence of causal search methods with brilliant scalability. Existing summaries of causal discovery methods mainly focus on traditional methods based on constraints, scores and FCMs, there is a lack of perfect sorting and elaboration for deep learning-based methods, also lacking some considers and exploration of causal discovery methods from the perspective of variable paradigms. Therefore, we divide the possible causal discovery tasks into three types according to the variable paradigm and give the definitions of the three tasks respectively, define and instantiate the relevant datasets for each task and the final causal model constructed at the same time, then reviews the main existing causal discovery methods for different tasks. Finally, we propose some roadmaps from different perspectives for the current research gaps in the field of causal discovery and point out future research directions.
Due to their increasing spread, confidence in neural network predictions became more and more important. However, basic neural networks do not deliver certainty estimates or suffer from over or under confidence. Many researchers have been working on understanding and quantifying uncertainty in a neural network's prediction. As a result, different types and sources of uncertainty have been identified and a variety of approaches to measure and quantify uncertainty in neural networks have been proposed. This work gives a comprehensive overview of uncertainty estimation in neural networks, reviews recent advances in the field, highlights current challenges, and identifies potential research opportunities. It is intended to give anyone interested in uncertainty estimation in neural networks a broad overview and introduction, without presupposing prior knowledge in this field. A comprehensive introduction to the most crucial sources of uncertainty is given and their separation into reducible model uncertainty and not reducible data uncertainty is presented. The modeling of these uncertainties based on deterministic neural networks, Bayesian neural networks, ensemble of neural networks, and test-time data augmentation approaches is introduced and different branches of these fields as well as the latest developments are discussed. For a practical application, we discuss different measures of uncertainty, approaches for the calibration of neural networks and give an overview of existing baselines and implementations. Different examples from the wide spectrum of challenges in different fields give an idea of the needs and challenges regarding uncertainties in practical applications. Additionally, the practical limitations of current methods for mission- and safety-critical real world applications are discussed and an outlook on the next steps towards a broader usage of such methods is given.
We consider the problem of explaining the predictions of graph neural networks (GNNs), which otherwise are considered as black boxes. Existing methods invariably focus on explaining the importance of graph nodes or edges but ignore the substructures of graphs, which are more intuitive and human-intelligible. In this work, we propose a novel method, known as SubgraphX, to explain GNNs by identifying important subgraphs. Given a trained GNN model and an input graph, our SubgraphX explains its predictions by efficiently exploring different subgraphs with Monte Carlo tree search. To make the tree search more effective, we propose to use Shapley values as a measure of subgraph importance, which can also capture the interactions among different subgraphs. To expedite computations, we propose efficient approximation schemes to compute Shapley values for graph data. Our work represents the first attempt to explain GNNs via identifying subgraphs explicitly and directly. Experimental results show that our SubgraphX achieves significantly improved explanations, while keeping computations at a reasonable level.
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