Abolfazl Safikhani

Mingliang Ma, Abolfazl Safikhani

Deep neural networks are powerful tools to model observations over time with non-linear patterns. Despite the widespread use of neural networks in such settings, most theoretical developments of deep neural networks are under the assumption of independent observations, and theoretical results for temporally dependent observations are scarce. To bridge this gap, we study theoretical properties of deep neural networks on modeling non-linear time series data. Specifically, non-asymptotic bounds for prediction error of (sparse) feed-forward neural network with ReLU activation function is established under mixing-type assumptions. These assumptions are mild such that they include a wide range of time series models including auto-regressive models. Compared to independent observations, established convergence rates have additional logarithmic factors to compensate for additional complexity due to dependence among data points. The theoretical results are supported via various numerical simulation settings as well as an application to a macroeconomic data set.

Tianshu Feng, Rohan Gnanaolivu, Abolfazl Safikhani et al.

Human cancers present a significant public health challenge and require the discovery of novel drugs through translational research. Transcriptomics profiling data that describes molecular activities in tumors and cancer cell lines are widely utilized for predicting anti-cancer drug responses. However, existing AI models face challenges due to noise in transcriptomics data and lack of biological interpretability. To overcome these limitations, we introduce VETE (Variational and Explanatory Transcriptomics Encoder), a novel neural network framework that incorporates a variational component to mitigate noise effects and integrates traceable gene ontology into the neural network architecture for encoding cancer transcriptomics data. Key innovations include a local interpretability-guided method for identifying ontology paths, a visualization tool to elucidate biological mechanisms of drug responses, and the application of centralized large scale hyperparameter optimization. VETE demonstrated robust accuracy in cancer cell line classification and drug response prediction. Additionally, it provided traceable biological explanations for both tasks and offers insights into the mechanisms underlying its predictions. VETE bridges the gap between AI-driven predictions and biologically meaningful insights in cancer research, which represents a promising advancement in the field.

Abhishek Kaul, Stergios B. Fotopoulos, Venkata K. Jandhyala et al.

We study a plug in least squares estimator for the change point parameter where change is in the mean of a high dimensional random vector under subgaussian or subexponential distributions. We obtain sufficient conditions under which this estimator possesses sufficient adaptivity against plug in estimates of mean parameters in order to yield an optimal rate of convergence $O_p(ξ^{-2})$ in the integer scale. This rate is preserved while allowing high dimensionality as well as a potentially diminishing jump size $ξ,$ provided $s\log (p\vee T)=o(\surd(Tl_T))$ or $s\log^{3/2}(p\vee T)=o(\surd(Tl_T))$ in the subgaussian and subexponential cases, respectively. Here $s,p,T$ and $l_T$ represent a sparsity parameter, model dimension, sampling period and the separation of the change point from its parametric boundary. Moreover, since the rate of convergence is free of $s,p$ and logarithmic terms of $T,$ it allows the existence of limiting distributions. These distributions are then derived as the {\it argmax} of a two sided negative drift Brownian motion or a two sided negative drift random walk under vanishing and non-vanishing jump size regimes, respectively. Thereby allowing inference of the change point parameter in the high dimensional setting. Feasible algorithms for implementation of the proposed methodology are provided. Theoretical results are supported with monte-carlo simulations.