Dimensionality Reduction for Stationary Time Series via Stochastic Nonconvex Optimization

Stochastic optimization naturally arises in machine learning. Efficient algorithms with provable guarantees, however, are still largely missing, when the objective function is nonconvex and the data points are dependent. This paper studies this fundamental challenge through a streaming PCA problem for stationary time series data. Specifically, our goal is to estimate the principle component of time series data with respect to the covariance matrix of the stationary distribution. Computationally, we propose a variant of Oja's algorithm combined with downsampling to control the bias of the stochastic gradient caused by the data dependency. Theoretically, we quantify the uncertainty of our proposed stochastic algorithm based on diffusion approximations. This allows us to prove the asymptotic rate of convergence and further implies near optimal asymptotic sample complexity. Numerical experiments are provided to support our analysis

Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. Our result provides sample complexity bounds for distribution estimation using diffusion models. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. Furthermore, the generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution. The convergence rate depends on the subspace dimension, indicating that diffusion models can circumvent the curse of data ambient dimensionality.Comment: 52 pages, 4 figure

A sensitive and rapid HPLC-DAD method for the determination of 3-hydroxy-1,2-dimethyl-4-pyridone and its distribution in rats

Purpose: To establish a sensitive and rapid method for the determination of the tissue distribution of 3-hydroxy-1,2-dimethyl-4-pyridone (L1) in vivo, and its plasma protein binding capacity.Methods: This study optimized a reverse-phase HPLC method for specific and sensitive determination of L1 as well as its plasma and tissue  distributions. The optimized method was used to determine the plasma protein-binding capacity of L1 in Wistar rats.Results: A rapid, sensitive and simple HPLC-DAD method was established for studying the plasma and tissue distribution of L1. Following TI  administration, its liver concentrations peaked at 60 min and 360min, followed 360 min later with peak level in the kidney (second highest). The L1 concentration was significantly lower after 360 min than after 60 min, and values of its mean binding to plasma proteins was 5.2 % at different L1 concentrations.Conclusion: These results indicate that L1 is a drug with rapid-absorption and rapid-elimination thath is distributed widely in vivo in rats. Moreover, the drug has a weak plasma protein-binding capacity. Keywords: 3-Hydroxy-1,2-dimethyl-4-pyridone, Distribution, Alzheimer’s disease, Therap

A senescence-based prognostic gene signature for colorectal cancer and identification of the role of SPP1-positive macrophages in tumor senescence

BackgroundSenescence is significantly associated with cancer prognosis. This study aimed to construct a senescence-related prognostic model for colorectal cancer (CRC) and to investigate the influence of senescence on the tumor microenvironment.MethodsTranscriptome and clinical data of CRC cases were downloaded from The Cancer Genome Atlas (TCGA) and Gene Expression Omnibus (GEO) databases. Senescence-related prognostic genes detected by univariate Cox regression were included in Least Absolute Shrinkage and Selection Operator (LASSO) analysis to construct a model. The efficacy of the model was validated using the receiver operating characteristic (ROC) curve and survival analysis. Differentially expressed genes (DEGs) were identified and Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway enrichment were performed. CIBERSORT and Immuno-Oncology Biological Research (IOBR) were used to investigate the features of the tumor microenvironment. Single-cell RNA-seq data were used to investigate the expression levels of model genes in various cell types. Immunofluorescence staining for p21, SPP1, and CD68 was performed with human colon tissues.ResultsA seven-gene (PTGER2, FGF2, IGFBP3, ANGPTL4, DKK1, WNT16 and SPP1) model was finally constructed. Patients were classified as high- or low-risk using the median score as the threshold. The area under the ROC curve (AUC) for the 1-, 2-, and 3-year disease-specific survival (DSS) were 0.731, 0.651, and 0.643, respectively. Survival analysis showed a better 5-year DSS in low-risk patients in the construction and validation cohorts. GO and KEGG analyses revealed that DEGs were enriched in extracellular matrix (ECM)-receptor interactions, focal adhesion, and protein digestion and absorption. CIBERSORT and IOBR analyses revealed an abundance of macrophages and an immunosuppressive environment in the high-risk subgroup. Low-risk patients had higher response rates to immunotherapy than high-risk patients. ScRNA-seq data revealed high expression of SPP1 in a subset of macrophages with strong senescence-associated secretory phenotype (SASP) features. Using CRC tumor tissues, we discovered that SPP1+ macrophages were surrounded by a large number of senescent tumor cells in high-grade tumors.ConclusionOur study presents a novel model based on senescence-related genes that can identify CRC patients with a poor prognosis and an immunosuppressive tumor microenvironment. SPP1+ macrophages may correlate with cell senescence leading to poor prognosis

Efficient RL with Impaired Observability: Learning to Act with Delayed and Missing State Observations

In real-world reinforcement learning (RL) systems, various forms of impaired observability can complicate matters. These situations arise when an agent is unable to observe the most recent state of the system due to latency or lossy channels, yet the agent must still make real-time decisions. This paper introduces a theoretical investigation into efficient RL in control systems where agents must act with delayed and missing state observations. We establish near-optimal regret bounds, of the form $\tilde{\mathcal{O}}(\sqrt{{\rm poly}(H) SAK})$, for RL in both the delayed and missing observation settings. Despite impaired observability posing significant challenges to the policy class and planning, our results demonstrate that learning remains efficient, with the regret bound optimally depending on the state-action size of the original system. Additionally, we provide a characterization of the performance of the optimal policy under impaired observability, comparing it to the optimal value obtained with full observability