In AI research and practice, rigor remains largely understood in terms of methodological rigor--such as whether mathematical, statistical, or computational methods are correctly applied. We argue that this narrow conception of rigor has contributed to the concerns raised by the responsible AI community, including overblown claims about the capabilities of AI systems. Our position is that a broader conception of what rigorous AI research and practice should entail is needed. We believe such a conception--in addition to a more expansive understanding of (1) methodological rigor--should include aspects related to (2) what background knowledge informs what to work on (epistemic rigor); (3) how disciplinary, community, or personal norms, standards, or beliefs influence the work (normative rigor); (4) how clearly articulated the theoretical constructs under use are (conceptual rigor); (5) what is reported and how (reporting rigor); and (6) how well-supported the inferences from existing evidence are (interpretative rigor). In doing so, we also provide useful language and a framework for much-needed dialogue about the AI community's work by researchers, policymakers, journalists, and other stakeholders.

Given a set of mixtures, blind source separation attempts to retrieve the source signals without or with very little information of the the mixing process. We present a geometric approach for blind separation of nonnegative linear mixtures termed {\em facet component analysis} (FCA). The approach is based on facet identification of the underlying cone structure of the data. Earlier works focus on recovering the cone by locating its vertices (vertex component analysis or VCA) based on a mutual sparsity condition which requires each source signal to possess a stand-alone peak in its spectrum. We formulate alternative conditions so that enough data points fall on the facets of a cone instead of accumulating around the vertices. To find a regime of unique solvability, we make use of both geometric and density properties of the data points, and develop an efficient facet identification method by combining data classification and linear regression. For noisy data, we show that denoising methods may be employed, such as the total variation technique in imaging processing, and principle component analysis. We show computational results on nuclear magnetic resonance spectroscopic data to substantiate our method.

Work in deep clustering focuses on finding a single partition of data.

We relate the problem of computing pointwise robustness of these networks to that of computing the maximum norm ball with a fixed center that can be contained in a non-convex polytope. This isachallenging problem ingeneral, howeverweshowthat there exists an efficient algorithm to compute this for polyhedral complices. Further we show that piecewise linear neural networks partition the input space into a polyhedralcomplex.

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