Papers by Andrew Mullhaupt
Entropy
We present an empirical estimator for the squared Hellinger distance between two continuous distr... more We present an empirical estimator for the squared Hellinger distance between two continuous distributions, which almost surely converges. We show that the divergence estimation problem can be solved directly using the empirical CDF and does not need the intermediate step of estimating the densities. We illustrate the proposed estimator on several one-dimensional probability distributions. Finally, we extend the estimator to a family of estimators for the family of α-divergences, which almost surely converge as well, and discuss the uniqueness of this result. We demonstrate applications of the proposed Hellinger affinity estimators to approximately bounding the Neyman–Pearson regions.
International Urogynecology Journal
Journal of Urology
urinary urgency sensation separately on numeric rating scales. We then compared their ratings of ... more urinary urgency sensation separately on numeric rating scales. We then compared their ratings of 0-10 (0[no symptom, 10[high symptom) of pain, pressure, discomfort and urgency and their correlations, to discover group differences between IC/BPS and OAB patients. RESULTS: Among IC/BPS patients, their mean numeric ratings of pain, pressure, or discomfort were almost identical (6.2AE2.3, 6.0AE2.1 and 6.6AE2.5 respectively). In addition, the three-way correlations between pain, pressure, or discomfort were very strong (all >0.77). The correlation between pain and discomfort ratings was extremely high at 0.95, suggesting that IC/BPS patients interpreted pain and discomfort as similar concepts and rated their intensity nearly identical. Among OAB patients, the correlations between pain and urgency (0.21) and between pressure and urgency (0.26) were very weak. The correlation between discomfort and urgency was moderate (0.45). OAB patients could distinguish urinary urgency from pain and pressure, but urgency and discomfort symptoms were less clear. CONCLUSIONS: IC/BPS patients interpreted bladder pain, pressure, or discomfort as the similar concepts and rated their intensity similarly. The concurrent use of three descriptors pain, pressure, or discomfort is reductant among IC/BPS. Bladder pain separated OAB from IC/BPS better than pressure or discomfort. OAB patients can distinguish urinary urgency from pain and pressure, but this is less clear cut between urgency and discomfort.
Neurourology and Urodynamics, 2022
Neurourology and Urodynamics, 2022
The increasing wealth of clinical data may become unmanageable for a physician to assimilate into... more The increasing wealth of clinical data may become unmanageable for a physician to assimilate into optimal decision‐making without assistance. Utilizing a novel machine learning (ML) approach, we sought to develop algorithms to predict patient outcomes following the overactive bladder treatments OnabotulinumtoxinA (OBTX‐A) injection and sacral neuromodulation (SNM).
We construct geometric shrinkage priors for Kählerian signal filters. Based on the characteristic... more We construct geometric shrinkage priors for Kählerian signal filters. Based on the characteristics of Kähler manifolds, an efficient and robust algorithm for finding superharmonic priors which outperform the Jeffreys prior is introduced. Several ansätze for the Bayesian predictive priors are also suggested. In particular, the ansätze related to Kähler potential are geometrically intrinsic priors to the information manifold of which the geometry is derived from the potential. The implication of the algorithm to time series models is also provided.
ArXiv, 2018
A new class of canonical forms is given proposed in which $(A, C)$ is in Hessenberg observer or S... more A new class of canonical forms is given proposed in which $(A, C)$ is in Hessenberg observer or Schur form and output normal: $\bf{I} - A^*A =C^*C$. Here, $C$ is the $d \times n$ measurement matrix and $A$ is the advance matrix. The $(C, A)$ stack is expressed as the product of $n$ orthogonal matrices, each of which depends on $d$ parameters. State updates require only ${\cal O}(nd)$ operations and derivatives of the system with respect to the parameters are fast and convenient to compute. Restrictions are given such that these models are generically identifiable. Since the observability Grammian is the identity matrix, system identification is better conditioned than other classes of models with fast updates.
Entropy, 2015
We prove the correspondence between the information geometry of a signal filter and a Kähler mani... more We prove the correspondence between the information geometry of a signal filter and a Kähler manifold. The information geometry of a minimum-phase linear system with a finite complex cepstrum norm is a Kähler manifold. The square of the complex cepstrum norm of the signal filter corresponds to the Kähler potential. The Hermitian structure of the Kähler manifold is explicitly emergent if and only if the impulse response function of the highest degree in z is constant in model parameters. The Kählerian information geometry takes advantage of more efficient calculation steps for the metric tensor and the Ricci tensor. Moreover, α-generalization on the geometric tensors is linear in α. It is also robust to find Bayesian predictive priors, such as superharmonic priors, because Laplace-Beltrami operators on Kähler manifolds are in much simpler forms than those of the non-Kähler manifolds. Several time series models are studied in the Kählerian information geometry.
Entropy, 2015
We construct geometric shrinkage priors for Kählerian signal filters. Based on the characteristic... more We construct geometric shrinkage priors for Kählerian signal filters. Based on the characteristics of Kähler manifolds, an efficient and robust algorithm for finding superharmonic priors which outperform the Jeffreys prior is introduced. Several ansätze for the Bayesian predictive priors are also suggested. In particular, the ansätze related to Kähler potential are geometrically intrinsic priors to the information manifold of which the geometry is derived from the potential. The implication of the algorithm to time series models is also provided.
AIP Conference Proceedings, 2015
We review the information geometry of linear systems and its application to Bayesian inference, a... more We review the information geometry of linear systems and its application to Bayesian inference, and the simplification available in the Kähler manifold case. We find conditions for the information geometry of linear systems to be Kähler, and the relation of the Kähler potential to information geometric quantities such as α-divergence, information distance and the dual αconnection structure. The Kähler structure simplifies the calculation of the metric tensor, connection, Ricci tensor and scalar curvature, and the α-generalization of the geometric objects. The Laplace-Beltrami operator is also simplified in the Kähler geometry. One of the goals in information geometry is the construction of Bayesian priors outperforming the Jeffreys prior, which we use to demonstrate the utility of the Kähler structure.
ABSTRACT Typescript. Thesis (Ph.D.)--New York University, Graduate School of Arts and Science, 19... more ABSTRACT Typescript. Thesis (Ph.D.)--New York University, Graduate School of Arts and Science, 1984. Includes bibliographic references.
Journal of Statistical Physics, 1985
Boolean delay equations (BDEs) are evolution equations for a vector of discrete variables x(t). T... more Boolean delay equations (BDEs) are evolution equations for a vector of discrete variables x(t). The value of each component xt(t), 0 or 1, depends on previous values of all components Xj(t-tiff, x~(t) = f,(xl(t-til),..., xn(t-tin)). BDEs model the evolution of biological and physical systems with threshold behavior and nonlinear feedbacks. The delays model distinct interaction times between pairs of variables. In this paper, BDEs are studied by algebraic, analytic, and numerical methods. It is shown that solutions depend continuously on the initial data and on the delays. BDEs are classified into conservative and dissipative. All BDEs with rational delays only have periodic solutions only. But conservative BDEs with rationally unrelated delays have aperiodic solutions of increasing complexity. These solutions can be approximated arbitrarily well by periodic solutions of increasing period. Self-similarity and intermittency of aperiodic solutions is studied as a function of delay values, and certain number-theoretic questions related to resonances and diophantine approximation are raised. Period length is shown to be a lower semicontinuous function of the delays for a given BDE, and can be evaluated explicitly for linear equations. We prove that a BDE is structurable stable if and only if it has eventually periodic solutions of bounded period, and if the length of initial transients is bounded. It is shown that, for dissipative BDEs, asymptotic solution behavior is typically governed by a reduced BDE. Applications to climate dynamics and other problems are outlined.
IEEE Transactions on Signal Processing, 1997
The adaptive identification of the impulse response of an innovation filter is considered. The im... more The adaptive identification of the impulse response of an innovation filter is considered. The impulse response is a finite sum of known basis functions with unknown coefficients. These unknown coefficients are estimated using a pseudolinear regression. This estimate is implemented using a square root algorithm based on a displacement rank structure. When the initial conditions have low displacement rank, the filter update is O(n). If the filter architecture is chosen to be triangular input balanced, the estimation problem is well-conditioned and a simple, low rank initialization is available.
IEEE Transactions on Signal Processing, 2004
The condition number of the n × n matrix P is examined, where P solves P − AP A * = BB * , and B ... more The condition number of the n × n matrix P is examined, where P solves P − AP A * = BB * , and B is a n × d matrix. Lower bounds on the condition number, κ, of P are given when A is normal, a single Jordan block or in Frobenius form. The bounds show that the illconditioning of P grows as exp(n/d) >> 1. These bounds are related to the condition number of the transformation that takes A to input normal form. A simulation shows that P is typically ill-conditioned in the case of n >> 1 and d = 1. When A ij has an independent Gaussian distribution (subject to restrictions), we observe that κ(P) 1/n ∼ 3.3. The effect of autocorrelated forcing on the conditioning on state space systems is examined.
IEEE Transactions on Automatic Control, 2001
An input pair (A, B) is triangular input normal if and only if A is triangular and AA * + BB * = ... more An input pair (A, B) is triangular input normal if and only if A is triangular and AA * + BB * = I n , where I n is the identity matrix. Input normal pairs generate an orthonormal basis for the impulse response. Every input pair may be transformed to a triangular input normal pair. A new system representation is given: (A, B) is triangular normal and A is a matrix fraction, A = M −1 N , where M and N are triangular matrices of low bandwidth. For single input pairs, M and N are bidiagonal and an explicit parameterization is given in terms of the eigenvalues of A. This band fraction structure allows for fast updates of state space systems and fast system identification. When A has only real eigenvalues, one state advance requires 3n multiplications for the single input case.
Discrete Mathematics, 1990
Climate Dynamics, 1987
A large fraction of climatic varability on the Quaternary time scale can be explained by nonlinea... more A large fraction of climatic varability on the Quaternary time scale can be explained by nonlinear interactions between the radiation balance of the global atmosphere-ocean system and the mass balance of Northern Hemisphere ice sheets. Recent analyses of paleoclimatic proxy data indicate a further important contribution to this variability from changes in deep-water formation occurring in the North Atlantic Subpolar Sea. We study the effects of these changes on variations in global temperature and ice volume characteristic of the late Quaternary. The novel framework of Boolean delay equations (BDEs) is used to formulate a conceptual model of the climatic system under study, and to analyze this formal model. Selfsustained oscillations in the intensity of the Atlantic Ocean's thermohaline circulation result from the interaction of sea-ice formation with the waxing and waning of continental ice sheets. The comparison of model results with paleoclimatic records suggests a considerable slowing down of the abyssal circulation during glacial episodes.
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Papers by Andrew Mullhaupt