In this paper, we extend the work of Liesen et al. (2002), which analyzes how the condition number of an orthonormal matrix Q changes when a column is added ([Q, c]), particularly focusing on the perpendicularity of c to the span of Q. Their result, presented in Theorem 2.3 of Liesen et al. (2002), assumes exact arithmetic and orthonormality of Q, which is a strong assumption when applying these results to numerical methods such as QR factorization algorithms. In our work, we address this gap by deriving bounds on the condition number increase for a matrix B without assuming perfect orthonormality, even when a column is not perfectly orthogonal to the span of B. This framework allows us to analyze QR factorization methods where orthogonalization is imperfect and subject to Gaussian noise. We also provide results on the performance of orthogonal projection and least squares under Gaussian noise, further supporting the development of this theory.
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If the probability model is correctly specified, then we can estimate the covariance matrix of the asymptotic maximum likelihood estimate distribution using either the first or second derivatives of the likelihood function. Therefore, if the determinants of these two different covariance matrix estimation formulas differ this indicates model misspecification. This misspecification detection strategy is the basis of the Determinant Information Matrix Test ($GIMT_{Det}$). To investigate the performance of the $GIMT_{Det}$, a Deterministic Input Noisy And gate (DINA) Cognitive Diagnostic Model (CDM) was fit to the Fraction-Subtraction dataset. Next, various misspecified versions of the original DINA CDM were fit to bootstrap data sets generated by sampling from the original fitted DINA CDM. The $GIMT_{Det}$ showed good discrimination performance for larger levels of misspecification. In addition, the $GIMT_{Det}$ did not detect model misspecification when model misspecification was not present and additionally did not detect model misspecification when the level of misspecification was very low. However, the $GIMT_{Det}$ discrimation performance was highly variable across different misspecification strategies when the misspecification level was moderately sized. The proposed new misspecification detection methodology is promising but additional empirical studies are required to further characterize its strengths and limitations.
In this study, we seek to understand how macroeconomic factors such as GDP, inflation, Unemployment Insurance, and S&P 500 index; as well as microeconomic factors such as health, race, and educational attainment impacted the unemployment rate for about 20 years in the United States. Our research question is to identify which factor(s) contributed the most to the unemployment rate surge using linear regression. Results from our studies showed that GDP (negative), inflation (positive), Unemployment Insurance (contrary to popular opinion; negative), and S&P 500 index (negative) were all significant factors, with inflation being the most important one. As for health issue factors, our model produced resultant correlation scores for occurrences of Cardiovascular Disease, Neurological Disease, and Interpersonal Violence with unemployment. Race as a factor showed a huge discrepancies in the unemployment rate between Black Americans compared to their counterparts. Asians had the lowest unemployment rate throughout the years. As for education attainment, results showed that having a higher education attainment significantly reduced one chance of unemployment. People with higher degrees had the lowest unemployment rate. Results of this study will be beneficial for policymakers and researchers in understanding the unemployment rate during the pandemic.
Deriving a priority vector from a pairwise comparison matrix (PCM) is a crucial step in the Analytical Hierarchy Process (AHP). Although there exists a priority vector that satisfies the conditions of order preservation (COP), the priority vectors obtained through existing prioritization methods frequently violate these conditions, resulting in numerous COP violations. To address this issue, this paper introduces a novel procedure to manage COP violations in AHP. Firstly, we prove that the index-exchangeability condition is both a necessary and sufficient condition for determining whether a priority vector satisfies COP. This enables the direct detection of COP violations, relying solely on the pairwise comparison preferences of decision-makers, rather than the prioritization methods utilized. Subsequently, we propose the Minimal Number of Violations and Deviations Method (MNVDM) model, which aims to derive a priority vector with the minimal number of COP violations. In particular, the MNVDM can obtain a violation-free priority vector when the PCM meets the index exchangeability conditions. Furthermore, an optimization model based on minimizing information loss is designed to ensure the COP by revising the preferences when the index-exchangeability conditions are violated. Finally, the feasibility and efficiency of the proposed models are validated through numerical examples and Monte Carlo simulation experiments. Our implementation is available at: //github.com/Tommytutu/COP.
In this paper, we explore a multi-task semantic communication (SemCom) system for distributed sources, extending the existing focus on collaborative single-task execution. We build on the cooperative multi-task processing introduced in [1], which divides the encoder into a common unit (CU) and multiple specific units (SUs). While earlier studies in multi-task SemCom focused on full observation settings, our research explores a more realistic case where only distributed partial observations are available, such as in a production line monitored by multiple sensing nodes. To address this, we propose an SemCom system that supports multi-task processing through cooperation on the transmitter side via split structure and collaboration on the receiver side. We have used an information-theoretic perspective with variational approximations for our end-to-end data-driven approach. Simulation results demonstrate that the proposed cooperative and collaborative multi-task (CCMT) SemCom system significantly improves task execution accuracy, particularly in complex datasets, if the noise introduced from the communication channel is not limiting the task performance too much. Our findings contribute to a more general SemCom framework capable of handling distributed sources and multiple tasks simultaneously, advancing the applicability of SemCom systems in real-world scenarios.
Artificial Intelligence (AI) research often aims to develop models that generalize reliably across complex datasets, yet this remains challenging in fields where data is scarce, intricate, or inaccessible. This paper introduces a novel approach leveraging three generative models of varying complexity to synthesize one of the most demanding structured datasets: Malicious Network Traffic. Our approach transforms numerical data into text, reframing data generation as a language modeling task, which enhances data regularization and significantly improves generalization and the quality of the synthetic data. Extensive statistical analyses demonstrate that our method surpasses state-of-the-art generative models in producing high-fidelity synthetic data. Additionally, we conduct a comprehensive study on synthetic data applications, effectiveness, and evaluation strategies, offering valuable insights into its role across various domains. Our code and pre-trained models are openly accessible at //github.com/Moe-Zbeeb/Exploring-the-landscape-for-generative-models-for-specialized-data-generation, enabling further exploration and application of our methodology. Index Terms: Data synthesis, machine learning, traffic generation, privacy-preserving data, generative models.
This study develops an algorithm to solve a variation of the Shortest Common Superstring (SCS) problem. There are two modifications to the base SCS problem. First, one string in the set S is allowed to have up to K mistakes, defined as not matching the SCS in at most K positions. Second, no string in S can be a substring of another in S. The algorithm proposed for the problem is exact.
Structured state-space models (SSMs) such as S4, stemming from the seminal work of Gu et al., are gaining popularity as effective approaches for modeling sequential data. Deep SSMs demonstrate outstanding performance across a diverse set of domains, at a reduced training and inference cost compared to attention-based transformers. Recent developments show that if the linear recurrence powering SSMs allows for multiplicative interactions between inputs and hidden states (e.g. GateLoop, Mamba, GLA), then the resulting architecture can surpass in both in accuracy and efficiency attention-powered foundation models trained on text, at scales of billion parameters. In this paper, we give theoretical grounding to this recent finding using tools from Rough Path Theory: we show that when random linear recurrences are equipped with simple input-controlled transitions (selectivity mechanism), then the hidden state is provably a low-dimensional projection of a powerful mathematical object called the signature of the input -- capturing non-linear interactions between tokens at distinct timescales. Our theory not only motivates the success of modern selective state-space models such as Mamba but also provides a solid framework to understand the expressive power of future SSM variants.
The fusion of causal models with deep learning introducing increasingly intricate data sets, such as the causal associations within images or between textual components, has surfaced as a focal research area. Nonetheless, the broadening of original causal concepts and theories to such complex, non-statistical data has been met with serious challenges. In response, our study proposes redefinitions of causal data into three distinct categories from the standpoint of causal structure and representation: definite data, semi-definite data, and indefinite data. Definite data chiefly pertains to statistical data used in conventional causal scenarios, while semi-definite data refers to a spectrum of data formats germane to deep learning, including time-series, images, text, and others. Indefinite data is an emergent research sphere inferred from the progression of data forms by us. To comprehensively present these three data paradigms, we elaborate on their formal definitions, differences manifested in datasets, resolution pathways, and development of research. We summarize key tasks and achievements pertaining to definite and semi-definite data from myriad research undertakings, present a roadmap for indefinite data, beginning with its current research conundrums. Lastly, we classify and scrutinize the key datasets presently utilized within these three paradigms.
Multimodality Representation Learning, as a technique of learning to embed information from different modalities and their correlations, has achieved remarkable success on a variety of applications, such as Visual Question Answering (VQA), Natural Language for Visual Reasoning (NLVR), and Vision Language Retrieval (VLR). Among these applications, cross-modal interaction and complementary information from different modalities are crucial for advanced models to perform any multimodal task, e.g., understand, recognize, retrieve, or generate optimally. Researchers have proposed diverse methods to address these tasks. The different variants of transformer-based architectures performed extraordinarily on multiple modalities. This survey presents the comprehensive literature on the evolution and enhancement of deep learning multimodal architectures to deal with textual, visual and audio features for diverse cross-modal and modern multimodal tasks. This study summarizes the (i) recent task-specific deep learning methodologies, (ii) the pretraining types and multimodal pretraining objectives, (iii) from state-of-the-art pretrained multimodal approaches to unifying architectures, and (iv) multimodal task categories and possible future improvements that can be devised for better multimodal learning. Moreover, we prepare a dataset section for new researchers that covers most of the benchmarks for pretraining and finetuning. Finally, major challenges, gaps, and potential research topics are explored. A constantly-updated paperlist related to our survey is maintained at //github.com/marslanm/multimodality-representation-learning.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
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