This work analyzes the subspace-constrained Tyler's estimator (STE) [12] designed for recovering a low-dimensional subspace within a dataset that may be highly corrupted with outliers. It assumes a weak inlier-outlier model and allows the fraction of inliers to be smaller than a fraction that leads to computational hardness of the robust subspace recovery problem. It shows that in this setting, if the initialization of STE, which is an iterative algorithm, satisfies a certain condition, then STE can effectively recover the underlying subspace. It further shows that under the generalized haystack model, STE initialized by the Tyler's M-estimator (TME), can recover the subspace when the fraction of iniliers is too small for TME to handle.

Recurrent Neural Networks (RNNs) have achieved tremendous success in processing sequential data, yet understanding and analyzing their behaviours remains a significant challenge. To this end, many efforts have been made to extract finite automata from RNNs, which are more amenable for analysis and explanation. However, existing approaches like exact learning and compositional approaches for model extraction have limitations in either scalability or precision. In this paper, we propose a novel framework of Weighted Finite Automata (WFA) extraction and explanation to tackle the limitations for natural language tasks. First, to address the transition sparsity and context loss problems we identified in WFA extraction for natural language tasks, we propose an empirical method to complement missing rules in the transition diagram, and adjust transition matrices to enhance the context-awareness of the WFA. We also propose two data augmentation tactics to track more dynamic behaviours of RNN, which further allows us to improve the extraction precision. Based on the extracted model, we propose an explanation method for RNNs including a word embedding method -- Transition Matrix Embeddings (TME) and TME-based task oriented explanation for the target RNN. Our evaluation demonstrates the advantage of our method in extraction precision than existing approaches, and the effectiveness of TME-based explanation method in applications to pretraining and adversarial example generation.

The foundation of our recommendation stack is a scoring model we call p(sale), which estimates the probability that any given client will purchase any given item. This model has gone through many iterations over the years, from a mixed effects model, to a matrix factorization model, and now to a novel sequence-based model. Internally we call this the Client Time Series Model (aka CTSM) because of its focus on the time-domain of client interactions. This post details our new model, which is a significant improvement for both the quality of our recommendations and the maintainability of our systems. Before setting out to develop our new model, it was clear that the evolution of our business necessitated a change to our modeling approach.

We investigated the data-driven relationship between features in the tumor microenvironment (TME) and the overall and 5-year survival in triple-negative breast cancer (TNBC) and non-TNBC (NTNBC) patients by using Explainable Artificial Intelligence (XAI) models. We used clinical information from patients with invasive breast carcinoma from The Cancer Genome Atlas and from two studies from the cbioPortal, the PanCanAtlas project and the GDAC Firehose study. In this study, we used a normalized RNA sequencing data-driven cohort from 1,015 breast cancer patients, alive or deceased, from the UCSC Xena data set and performed integrated deconvolution with the EPIC method to estimate the percentage of seven different immune and stromal cells from RNA sequencing data. Novel insights derived from our XAI model showed that CD4+ T cells and B cells are more critical than other TME features for enhanced prognosis for both TNBC and NTNBC patients. Our XAI model revealed the critical inflection points (i.e., threshold fractions) of CD4+ T cells and B cells above or below which 5-year survival rates improve. Subsequently, we ascertained the conditional probabilities of $\geq$ 5-year survival in both TNBC and NTNBC patients under specific conditions inferred from the inflection points. In particular, the XAI models revealed that a B-cell fraction exceeding 0.018 in the TME could ensure 100% 5-year survival for NTNBC patients. The findings from this research could lead to more accurate clinical predictions and enhanced immunotherapies and to the design of innovative strategies to reprogram the TME of breast cancer patients.

A disease capable of decimating and killing those affected, cancer involves cells in a specific part of the body growing and reproducing uncontrollably in a process known as proliferation. In a recent breakthrough, the tumor microenvironment (TME) has been established as a key driver for cancer progression, promoting resistance to therapeutics all the while enabling the disease to evade the immune system. Specifically, myeloid-derived suppressor cells (MDSCs) have been shown to play a central role in maintaining the TME through the suppression of host immunity, the establishment of new vasculature, and the remodeling of connective tissue to support tumor growth. Therefore, it is imperative to develop cancer immunotherapies able to promote the anti-oncological activity of the immune system with the dual ability to combat the highly detrimental effects of the TME. However, while it is straightforward to assess the effect of new therapies on cancer cells, estimating the effectiveness of these novel therapies on the TME is challenging.