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1. Shared Information for a Markov Chain on a Tree

   https://doi.org/10.1109/TIT.2024.3353769  

   Bhattacharya, Sagnik; Narayan, Prakash (January 2024, IEEE Transactions on Information Theory)

   Veeravalli, V. V. (Ed.)

   Abstract—Shared information is a measure of mutual de- pendence among multiple jointly distributed random variables with finite alphabets. For a Markov chain on a tree with a given joint distribution, we give a new proof of an explicit characterization of shared information. The Markov chain on a tree is shown to possess a global Markov property based on graph separation; this property plays a key role in our proofs. When the underlying joint distribution is not known, we exploit the special form of this characterization to provide a multiarmed bandit algorithm for estimating shared information, and analyze its error performance. 

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2. Potential conditional mutual information: Estimators and properties

   https://doi.org/10.1109/ALLERTON.2017.8262877  

   Rahimzamani, Arman; Kannan, Sreeram (October 2017, Communication, Control, and Computing (Allerton), 2017 55th Annual Allerton Conference on)

   The conditional mutual information I(X; Y|Z) measures the average information that X and Y contain about each other given Z. This is an important primitive in many learning problems including conditional independence testing, graphical model inference, causal strength estimation and time-series problems. In several applications, it is desirable to have a functional purely of the conditional distribution py|x, z rather than of the joint distribution pX, Y, Z. We define the potential conditional mutual information as the conditional mutual information calculated with a modified joint distribution pY|X, ZqX, Z, where qX, Z is a potential distribution, fixed airport. We develop K nearest neighbor based estimators for this functional, employing importance sampling, and a coupling trick, and prove the finite k consistency of such an estimator. We demonstrate that the estimator has excellent practical performance and show an application in dynamical system inference. 

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3. Hyperalignment: Modeling shared information encoded in idiosyncratic cortical topographies

   https://doi.org/10.7554/eLife.56601  

   Haxby, James V; Guntupalli, J Swaroop; Nastase, Samuel A; Feilong, Ma (June 2020, eLife)

   Information that is shared across brains is encoded in idiosyncratic fine-scale functional topographies. Hyperalignment captures shared information by projecting pattern vectors for neural responses and connectivities into a common, high-dimensional information space, rather than by aligning topographies in a canonical anatomical space. Individual transformation matrices project information from individual anatomical spaces into the common model information space, preserving the geometry of pairwise dissimilarities between pattern vectors, and model cortical topography as mixtures of overlapping, individual-specific topographic basis functions, rather than as contiguous functional areas. The fundamental property of brain function that is preserved across brains is information content, rather than the functional properties of local features that support that content. In this Perspective, we present the conceptual framework that motivates hyperalignment, its computational underpinnings for joint modeling of a common information space and idiosyncratic cortical topographies, and discuss implications for understanding the structure of cortical functional architecture. 

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4. An Econometric Model of International Growth Dynamics for Long-horizon Forecasting

   Ulrich K. Müller, James H. (September 2022, The review of economics and statistics)

   We develop a Bayesian latent factor model of the joint long-run evolution of GDP per capita for 113 countries over the 118 years from 1900 to 2017. We find considerable heterogeneity in rates of convergence, including rates for some countries that are so slow that they might not converge (or diverge) in century-long samples, and a sparse correlation pattern (“convergence clubs”) between countries. The joint Bayesian structure allows us to compute a joint predictive distribution for the output paths of these countries over the next 100 years. This predictive distribution can be used for simulations requiring projections into the deep future, such as estimating the costs of climate change. The model’s pooling of information across countries results in tighter prediction intervals than are achieved using univariate information sets. Still, even using more than a century of data on many countries, the 100-year growth paths exhibit very wide uncertainty. 

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5. Effect of Spatial and Spectral Scaling on Joint Characterization of the Spectral Mixture Residual: Comparative Analysis of AVIRIS and WorldView-3 SWIR for Geologic Mapping in Anza-Borrego Desert State Park

   https://doi.org/10.3390/s23156742  

   Price, Jeffrey; Sousa, Daniel; Sousa, Francis J. (August 2023, Sensors)

   A geologic map is both a visual depiction of the lithologies and structures occurring at the Earth’s surface and a representation of a conceptual model for the geologic history in a region. The work needed to capture such multifaced information in an accurate geologic map is time consuming. Remote sensing can complement traditional primary field observations, geochemistry, chronometry, and subsurface geophysical data in providing useful information to assist with the geologic mapping process. Two novel sources of remote sensing data are particularly relevant for geologic mapping applications: decameter-resolution imaging spectroscopy (spectroscopic imaging) and meter-resolution multispectral shortwave infrared (SWIR) imaging. Decameter spectroscopic imagery can capture important mineral absorptions but is frequently unable to spatially resolve important geologic features. Meter-resolution multispectral SWIR images are better able to resolve fine spatial features but offer reduced spectral information. Such disparate but complementary datasets can be challenging to integrate into the geologic mapping process. Here, we conduct a comparative analysis of spatial and spectral scaling for two such datasets: one Airborne Visible/Infrared Imaging Spectrometer—Classic (AVIRIS-classic) flightline, and one WorldView-3 (WV3) scene, for a geologically complex landscape in Anza-Borrego Desert State Park, California. To do so, we use a two-stage framework that synthesizes recent advances in the spectral mixture residual and joint characterization. The mixture residual uses the wavelength-explicit misfit of a linear spectral mixture model to capture low variance spectral signals. Joint characterization utilizes nonlinear dimensionality reduction (manifold learning) to visualize spectral feature space topology and identify clusters of statistically similar spectra. For this study area, the spectral mixture residual clearly reveals greater spectral dimensionality in AVIRIS than WorldView (99% of variance in 39 versus 5 residual dimensions). Additionally, joint characterization shows more complex spectral feature space topology for AVIRIS than WorldView, revealing information useful to the geologic mapping process in the form of mineralogical variability both within and among mapped geologic units. These results illustrate the potential of recent and planned imaging spectroscopy missions to complement high-resolution multispectral imagery—along with field and lab observations—in planning, collecting, and interpreting the results from geologic field work. 

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