A class of occupancy models for detection/non-detection data is proposed to relax the closure assumption of N$-$mixture models. We introduce a community parameter $c$, ranging from $0$ to $1$, which characterizes a certain portion of individuals being fixed across multiple visits. As a result, when $c$ equals $1$, the model reduces to the N$-$mixture model; this reduced model is shown to overestimate abundance when the closure assumption is not fully satisfied. Additionally, by including a zero-inflated component, the proposed model can bridge the standard occupancy model ($c=0$) and the zero-inflated N$-$mixture model ($c=1$). We then study the behavior of the estimators for the two extreme models as $c$ varies from $0$ to $1$. An interesting finding is that the zero-inflated N$-$mixture model can consistently estimate the zero-inflated probability (occupancy) as $c$ approaches $0$, but the bias can be positive, negative, or unbiased when $c>0$ depending on other parameters. We also demonstrate these results through simulation studies and data analysis.
相關內容
Text-to-Image diffusion models have made tremendous progress over the past two years, enabling the generation of highly realistic images based on open-domain text descriptions. However, despite their success, text descriptions often struggle to adequately convey detailed controls, even when composed of long and complex texts. Moreover, recent studies have also shown that these models face challenges in understanding such complex texts and generating the corresponding images. Therefore, there is a growing need to enable more control modes beyond text description. In this paper, we introduce Uni-ControlNet, a novel approach that allows for the simultaneous utilization of different local controls (e.g., edge maps, depth map, segmentation masks) and global controls (e.g., CLIP image embeddings) in a flexible and composable manner within one model. Unlike existing methods, Uni-ControlNet only requires the fine-tuning of two additional adapters upon frozen pre-trained text-to-image diffusion models, eliminating the huge cost of training from scratch. Moreover, thanks to some dedicated adapter designs, Uni-ControlNet only necessitates a constant number (i.e., 2) of adapters, regardless of the number of local or global controls used. This not only reduces the fine-tuning costs and model size, making it more suitable for real-world deployment, but also facilitate composability of different conditions. Through both quantitative and qualitative comparisons, Uni-ControlNet demonstrates its superiority over existing methods in terms of controllability, generation quality and composability. Code is available at \url{//github.com/ShihaoZhaoZSH/Uni-ControlNet}.
While transformers have shown remarkable success in natural language processing, their attention mechanism's large memory requirements have limited their ability to handle longer contexts. Prior approaches, such as recurrent memory or retrieval-based augmentation, have either compromised the random-access flexibility of attention (i.e., the capability to select any token in the entire context) or relied on separate mechanisms for relevant context retrieval, which may not be compatible with the model's attention. In this paper, we present a novel approach that allows access to the complete context while retaining random-access flexibility, closely resembling running attention on the entire context. Our method uses a landmark token to represent each block of the input and trains the attention to use it for selecting relevant blocks, enabling retrieval of blocks directly through the attention mechanism instead of by relying on a separate mechanism. Our approach seamlessly integrates with specialized data structures and the system's memory hierarchy, enabling processing of arbitrarily long context lengths. We demonstrate that our method can obtain comparable performance with Transformer-XL while significantly reducing the number of retrieved tokens in each step. Finally, we show that fine-tuning LLaMA 7B with our method successfully extends its context length capacity up to 32k tokens, allowing for inference at the context lengths of GPT-4.
We study the problem of decentralized power allocation in a multi-access channel (MAC) with non-cooperative users, additive noise of arbitrary distribution and a generalized power constraint, i.e., the transmit power constraint is modeled by an upper bound on $\mathbb{E}[\phi(|S|)]$, where $S$ is the transmit signal and $\phi(.)$ is some non-negative, increasing and bounded function. The generalized power constraint captures the notion of power for different wireless signals such as RF, optical, acoustic, etc. We derive the optimal power allocation policy when there a large number of non-cooperative users in the MAC. Further, we show that, once the number of users in the MAC crosses a finite threshold, the proposed power allocation policy of all users is optimal and remains invariant irrespective of the actual number of users. We derive the above results under the condition that the entropy power of the MAC, $e^{2h(S)+c}$, is strictly convex, where $h(S)$ is the maximum achievable entropy of the transmit signal and $c$ is a finite constant corresponding to the entropy of the additive noise.
In this paper, we propose a new model for forecasting time series data distributed on a matrix-shaped spatial grid, using the historical spatio-temporal data together with auxiliary vector-valued time series data. We model the matrix time series as an auto-regressive process, where a future matrix is jointly predicted by the historical values of the matrix time series as well as an auxiliary vector time series. The matrix predictors are associated with row/column-specific autoregressive matrix coefficients that map the predictors to the future matrices via a bi-linear transformation. The vector predictors are mapped to matrices by taking mode product with a 3D coefficient tensor. Given the high dimensionality of the tensor coefficient and the underlying spatial structure of the data, we propose to estimate the tensor coefficient by estimating one functional coefficient for each covariate, with 2D input domain, from a Reproducing Kernel Hilbert Space. We jointly estimate the autoregressive matrix coefficients and the functional coefficients under a penalized maximum likelihood estimation framework, and couple it with an alternating minimization algorithm. Large sample asymptotics of the estimators are established and performances of the model are validated with extensive simulation studies and a real data application to forecast the global total electron content distributions.
PCA-Net is a recently proposed neural operator architecture which combines principal component analysis (PCA) with neural networks to approximate operators between infinite-dimensional function spaces. The present work develops approximation theory for this approach, improving and significantly extending previous work in this direction: First, a novel universal approximation result is derived, under minimal assumptions on the underlying operator and the data-generating distribution. Then, two potential obstacles to efficient operator learning with PCA-Net are identified, and made precise through lower complexity bounds; the first relates to the complexity of the output distribution, measured by a slow decay of the PCA eigenvalues. The other obstacle relates to the inherent complexity of the space of operators between infinite-dimensional input and output spaces, resulting in a rigorous and quantifiable statement of the curse of dimensionality. In addition to these lower bounds, upper complexity bounds are derived. A suitable smoothness criterion is shown to ensure an algebraic decay of the PCA eigenvalues. Furthermore, it is shown that PCA-Net can overcome the general curse of dimensionality for specific operators of interest, arising from the Darcy flow and the Navier-Stokes equations.
The article discusses the localization of radiation sources whose number and other relevant parameters are not known in advance. The data collection is ensured by an autonomous mobile robot that performs a survey in a defined region of interest populated with static obstacles. The measurement trajectory is information-driven rather than pre-planned. The localization exploits a regularized particle filter estimating the sources' parameters continuously. The dynamic robot control switches between two modes, one attempting to minimize the Shannon entropy and the other aiming to reduce the variance of expected measurements in unexplored parts of the target area; both of the modes maintain safe clearance from the obstacles. The performance of the algorithms was tested in a simulation study based on real-world data acquired previously from three radiation sources exhibiting various activities. Our approach reduces the time necessary to explore the region and to find the sources by approximately 40 %; at present, however, the method is unable to reliably localize sources that have a relatively low intensity. In this context, additional research has been planned to increase the credibility and robustness of the procedure and to improve the robotic platform autonomy.
We study implementations of basic fault-tolerant primitives, such as consensus and registers, in message-passing systems subject to process crashes and a broad range of communication failures. Our results characterize the necessary and sufficient conditions for implementing these primitives as a function of the connectivity constraints and synchrony assumptions. Our main contribution is a new algorithm for partially synchronous consensus that is resilient to process crashes and channel failures and is optimal in its connectivity requirements. In contrast to prior work, our algorithm assumes the most general model of message loss where faulty channels are flaky, i.e., can lose messages without any guarantee of fairness. This failure model is particularly challenging for consensus algorithms, as it rules out standard solutions based on leader oracles and failure detectors. To circumvent this limitation, we construct our solution using a new variant of the recently proposed view synchronizer abstraction, which we adapt to the crash-prone setting with flaky channels.
This paper investigates Gaussian copula mixture models (GCMM), which are an extension of Gaussian mixture models (GMM) that incorporate copula concepts. The paper presents the mathematical definition of GCMM and explores the properties of its likelihood function. Additionally, the paper proposes extended Expectation Maximum algorithms to estimate parameters for the mixture of copulas. The marginal distributions corresponding to each component are estimated separately using nonparametric statistical methods. In the experiment, GCMM demonstrates improved goodness-of-fitting compared to GMM when using the same number of clusters. Furthermore, GCMM has the ability to leverage un-synchronized data across dimensions for more comprehensive data analysis.
This paper provides the first sample complexity lower bounds for the estimation of simple diffusion models, including the Bass model (used in modeling consumer adoption) and the SIR model (used in modeling epidemics). We show that one cannot hope to learn such models until quite late in the diffusion. Specifically, we show that the time required to collect a number of observations that exceeds our sample complexity lower bounds is large. For Bass models with low innovation rates, our results imply that one cannot hope to predict the eventual number of adopting customers until one is at least two-thirds of the way to the time at which the rate of new adopters is at its peak. In a similar vein, our results imply that in the case of an SIR model, one cannot hope to predict the eventual number of infections until one is approximately two-thirds of the way to the time at which the infection rate has peaked. This lower bound in estimation further translates into a lower bound in regret for decision-making in epidemic interventions. Our results formalize the challenge of accurate forecasting and highlight the importance of incorporating additional data sources. To this end, we analyze the benefit of a seroprevalence study in an epidemic, where we characterize the size of the study needed to improve SIR model estimation. Extensive empirical analyses on product adoption and epidemic data support our theoretical findings.
Overlapping instruction subsets derived from human originated code have previously been shown to dramatically shrink the inductive programming search space, often by many orders of magnitude. Here we extend the instruction subset approach to consider direct instruction-instruction applications (or instruction digrams) as an additional search heuristic for inductive programming. In this study we analyse the frequency distribution of instruction digrams in a large sample of open source code. This indicates that the instruction digram distribution is highly skewed with over 93% of possible instruction digrams not represnted in the code sample. We demonstrate that instruction digrams can be used to constrain instruction selection during search, further reducing size of the the search space, in some cases by several orders of magnitude. This significantly increases the size of programs that can be generated using search based inductive programming techniques. We discuss the results and provide some suggestions for further work.
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