Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

Image_2_The role of Angiogenesis and remodeling (AR) associated signature for predicting prognosis and clinical outcome of immunotherapy in pan-cancer.tif

BackgroundAngiogenesis and remodeling (AR) is necessary for the growth and metastasis of cancers. Although AR related genes involved in this process are reported, the correlation between AR and clinical outcome, immune cell infiltration, and immunotherapy is still unknown in diverse cancers. This study aimed to investigate the role of AR in the tumor immune microenvironment (TIME) in pan-cancer, and explore its values in prognostic prediction and therapeutic responses.MethodsFirstly, AR genes (including angiogenesis genes and blood vessel remodeling genes) are collected from MsigDB database. The differential expression, and prognostic value of AR genes were studied in 33 tumor types based on TCGA and GTEx data. The AR score of each sample was calculated using the “ssGSEA” function of R package “GSVA” in pan-cancer. The correlation of the AR score with TIME index, such as the amount of stromal and immune components and the immune cell infiltration, was evaluated via integrating multiple computational methods. And we also utilized IMvigor210 and GSE78220 data to explore the prediction value of the AR score on the immunotherapy response.ResultsSignificant differences in AR gene expression between tumors and adjacent normal tissues were found in most cancer types. The AR score varied depending on the types of tumors, and high score was related to worse survival in various tumors, such as pancreatic and stomach adenocarcinoma and so on. Moreover, the AR score was further explored to be positively correlated with proportions and pathways of immune and stromal in TIME. And the AR score was positively correlated with immunosuppressive cells, including TAMs and iTregs, while negatively with CD8+ T cells. Further analysis revealed that patients with high AR had worse therapy efficacy and survival status in bladder cancer and melanomas.ConclusionsOur systematic analysis revealed that AR is closely associated TIME, and prognosis, and clinical characteristics in multiple cancers. Targeting AR genes may activate immune microenvironment and increase the efficacy of immunotherapy.</p

Table_1_The role of Angiogenesis and remodeling (AR) associated signature for predicting prognosis and clinical outcome of immunotherapy in pan-cancer.docx

BackgroundAngiogenesis and remodeling (AR) is necessary for the growth and metastasis of cancers. Although AR related genes involved in this process are reported, the correlation between AR and clinical outcome, immune cell infiltration, and immunotherapy is still unknown in diverse cancers. This study aimed to investigate the role of AR in the tumor immune microenvironment (TIME) in pan-cancer, and explore its values in prognostic prediction and therapeutic responses.MethodsFirstly, AR genes (including angiogenesis genes and blood vessel remodeling genes) are collected from MsigDB database. The differential expression, and prognostic value of AR genes were studied in 33 tumor types based on TCGA and GTEx data. The AR score of each sample was calculated using the “ssGSEA” function of R package “GSVA” in pan-cancer. The correlation of the AR score with TIME index, such as the amount of stromal and immune components and the immune cell infiltration, was evaluated via integrating multiple computational methods. And we also utilized IMvigor210 and GSE78220 data to explore the prediction value of the AR score on the immunotherapy response.ResultsSignificant differences in AR gene expression between tumors and adjacent normal tissues were found in most cancer types. The AR score varied depending on the types of tumors, and high score was related to worse survival in various tumors, such as pancreatic and stomach adenocarcinoma and so on. Moreover, the AR score was further explored to be positively correlated with proportions and pathways of immune and stromal in TIME. And the AR score was positively correlated with immunosuppressive cells, including TAMs and iTregs, while negatively with CD8+ T cells. Further analysis revealed that patients with high AR had worse therapy efficacy and survival status in bladder cancer and melanomas.ConclusionsOur systematic analysis revealed that AR is closely associated TIME, and prognosis, and clinical characteristics in multiple cancers. Targeting AR genes may activate immune microenvironment and increase the efficacy of immunotherapy.</p

Image_1_The role of Angiogenesis and remodeling (AR) associated signature for predicting prognosis and clinical outcome of immunotherapy in pan-cancer.pdf

BackgroundAngiogenesis and remodeling (AR) is necessary for the growth and metastasis of cancers. Although AR related genes involved in this process are reported, the correlation between AR and clinical outcome, immune cell infiltration, and immunotherapy is still unknown in diverse cancers. This study aimed to investigate the role of AR in the tumor immune microenvironment (TIME) in pan-cancer, and explore its values in prognostic prediction and therapeutic responses.MethodsFirstly, AR genes (including angiogenesis genes and blood vessel remodeling genes) are collected from MsigDB database. The differential expression, and prognostic value of AR genes were studied in 33 tumor types based on TCGA and GTEx data. The AR score of each sample was calculated using the “ssGSEA” function of R package “GSVA” in pan-cancer. The correlation of the AR score with TIME index, such as the amount of stromal and immune components and the immune cell infiltration, was evaluated via integrating multiple computational methods. And we also utilized IMvigor210 and GSE78220 data to explore the prediction value of the AR score on the immunotherapy response.ResultsSignificant differences in AR gene expression between tumors and adjacent normal tissues were found in most cancer types. The AR score varied depending on the types of tumors, and high score was related to worse survival in various tumors, such as pancreatic and stomach adenocarcinoma and so on. Moreover, the AR score was further explored to be positively correlated with proportions and pathways of immune and stromal in TIME. And the AR score was positively correlated with immunosuppressive cells, including TAMs and iTregs, while negatively with CD8+ T cells. Further analysis revealed that patients with high AR had worse therapy efficacy and survival status in bladder cancer and melanomas.ConclusionsOur systematic analysis revealed that AR is closely associated TIME, and prognosis, and clinical characteristics in multiple cancers. Targeting AR genes may activate immune microenvironment and increase the efficacy of immunotherapy.</p