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NASA NTRSDate not supplied

Understanding the Impact of Unobservable Variables on the Performance of Predictive Models: The Need for Feature Space Partitioning and Fusion

When developing predictive models over a dataset, the model is globally optimized across the entire feature space to learn a decision boundary. However, when unobservable variables—which cannot be measured or estimated—interact with the observable variables, this can negatively impact the optimization applied to the decision boundary since the data samples introduced by unobservable variables may have little to no association with the applied global optimization. This, consequently, penalizes the entire decision boundary and model performance. This paper examines some of the detrimental effects of unobservable variables, particularly their role in creating new modes in the distribution of observable variables and reducing the separability of class distributions. Such challenges result in skewed or warped decision boundaries and decreased accuracy of model predictions, particularly for interpretable models like logistic regression and decision trees. Through two illustrative case examples, we highlight the need to address the challenges imposed by unobservable variables. We propose a strategy to mitigate these challenges by creating local regions within the feature space through partitioning. This enables the optimization of local models within the regions to overcome the impact of unobservability in different feature space localities. Research into a more sophisticated partitioning strategy and where the partition should be relative to the sample of interest is left as future work. Through the analysis of the impact of unobservability and the development of a partitioning method, we demonstrate the clear need for a partitioning strategy that integrates knowledge from multiple local models to estimate risk factors using information fusion. Thus, we establish the foundation and motivation for using partitioning and information fusion to overcome the effects of unobservability in predictive models. Formal fusion methods, such as Dempster-Shafer theory, can better leverage the information from local regions to improve the performance of interpretable predictive models in the presence of unobservable variables.

Time Series Data↗
NASA NTRS1977

Indirect observation of unobservable interstellar molecules

It is suggested that the abundances of neutral non-polar interstellar molecules unobservable by radio astronomy can be systematically determined by radio observation of the protonated ions. As an example, observed N2H(+) column densities are analyzed to infer molecular nitrogen abundances in dense interstellar clouds. The chemistries and expected densities of the protonated ions of O2, C2, CO2, C2H2 and CH4 are then discussed. Microwave transition frequencies fo HCO2(+) and C2H3(+) are estimated, and a preliminary astronomical search for HCO2(+) is described.

Herbst, E.↗
NASA NTRS1977

Indirect observation of unobservable interstellar molecules

It is suggested that the abundances of neutral nonpolar interstellar molecules unobservable by radio astronomy can be systematically determined by radio observation of the protonated ions. As an example, observed N2H(+) column densities are analyzed to infer molecular nitrogen abundances in dense interstellar clouds. The chemistries and expected densities of the protonated ions of O2, C2, CO2, C2H2, and CH4 are then discussed. Microwave transition frequencies for HCO2(+) and C2H3(+) are estimated, and a preliminary astronomical search for HCO2(+) is described.

Herbst, E.↗
NASA NTRS2020

Global Airborne Sampling Reveals a Previously Unobserved Dimethyl Sulfide Oxidation Mechanism in the Marine Atmosphere

Dimethyl sulfide (DMS), emitted from the oceans, is the most abundant biological source of sulfur to the marine atmosphere. Atmospheric DMS is oxidized to condensable products that form secondary aerosols that affect Earth’s radiative balance by scattering solar radiation and serving as cloud condensation nuclei. We report the atmospheric discovery of a previously unquantified DMS oxidation product, hydroperoxymethyl thioformate (HPMTF, HOOCH2SCHO), identified through global-scale airborne observations that demonstrate it to be a major reservoir of marine sulfur. Observationally constrained model results show that more than 30% of oceanic DMS emitted to the atmosphere forms HPMTF. Coincident particle measurements suggest a strong link between HPMTF concentration and new particle formation and growth. Analyses of these observations show that HPMTF chemistry must be included in atmospheric models to improve representation of key linkages between the biogeochemistry of the ocean, marine aerosol formation and growth, and their combined effects on climate.

DMS gas-phase oxidation product↗
NASA NTRS1980

Reduced-order Kalman filtering with incomplete observability

Kalman filtering is considered with reference to linear stochastic dynamic systems without complete observability. It is shown that the canonical decomposition theorem can be extended to the stochastic case and the matrix Riccati equation of the Kalman filter is order-reducible if some states are not observable. The inclusion of unobservable states in Kalman filtering makes the unobservable states 'asymptotically' observable in the filter if these unobservable states are dynamically connected to observable states and asymptotically stable. The reduced-order Kalman filter saves computation time when compared to the conventional Kalman filter.

Yonezawa, K.↗
NASA NTRS1990

A simulation survey of galaxy interactions

Many carefully selected samples of interacting galaxies have been observed extensively in attempts to clarify whether interaction produces activity in galaxies. Because the sample members represent a wide range of encounter parameters and times, one can then study whether there are correlations between observable encounter features and, for example, Seyfert activity. On the other hand, in theoretical studies, simulations typically deal with either time-consuming detailed modelling of single galaxy pairs or tracing a few model encounters over time. The authors extend the observational survey approach by combining it with a simulation survey. The authors are conducting a survey of model encounters, covering the most important encounter parameters over a wide range. Some parameters, such as companion structure and initial velocity, are demonstratably less important and can be ignored in a first pass. The parameter range must be richly enough sampled so that the authors can evaluate the uniqueness of the observable morphology and velocity structure of the resulting simulated pairs to diagnose unobservable companion orbit parameters. They are using a self-gravitating polar n-body code run on the Cray X-MP at the Alabama Supercomputer Network. For each simulation, the authors have stellar and gas distributions predicted over, typically, a billion years, along with information on gas motions within the disk and any material captured by the companion or lost to the system. Features of disturbed spiral galaxies are sensitive enough to time and encounter parameters so that a match of the simulation survey results to observations can be applied as starting points to infer unobservable orbital or system parameters in actual sample members. This should enable them to examine whether interesting observed properties (Seyfert activity, nuclear star-formation rate) are functions of unobservable dynamical properties which characterize each encounter. Any correlations (or lack of some expected ones) will provide strong clues as to how or whether these phenomena are related to interactions. Aside from its use with such observed samples, this survey should greatly speed determination of initial orbital parameters for more detailed subsequent simulations of individual systems.

Byrd, Gene G.↗
NASA NTRS1973

Reaction Li-6/p, pt/ at 590 MeV.

A lithium target enriched to 95.6 per cent of Li-6 and 0.685 cm thick was bombarded in the 590-MeV proton beam of a synchrocyclotron. Coincident events were detected in a double telescope arrangement. The characteristics of the unobserved three-nucleon residual system calculated for each event include the missing energy, the longitudinal recoil, and the transverse recoil. The cross-section data obtained indicate that zero recoil momentum for the unobserved three-nucleon recoil system is the most likely situation.

Dollhopf, W.↗
NASA NTRS1974

Attitude control concepts for precision-pointing nonrigid spacecraft

Literal criteria are developed for the controllability and observability of general models of flexible spacecraft. Results are interpreted in special cases and in physical terms, permitting in some cases the identification of uncontrollable and unobservable states simply by examination of scalars composed of modal parameters and location matrices for sensors and actuators. A procedure is established for isolation of uncontrollable states, whereby sensor and actuator configurations assure that uncontrollable flexible mode states are also unobservable; in many applications such states can then be removed by coordinate truncation.

Likins, P. W.↗
NASA NTRS1974

The influence of spacecraft flexibility on system controllability and observability

Literal criteria are developed for the controllability and observability of general models of flexible spacecraft. Results are interpreted in special cases and in physical terms, permitting in some cases the identification of uncontrollable and unobservable states simply by examination of scalars composed of modal parameters and location matrices for sensors and actuators. A procedure is established for isolation of uncontrollable states, whereby sensor and actuator configuration assure that uncontrollable flexible mode states are also unobservable; in many applications such states can then be removed by coordinate truncation.

Ohkami, Y.↗
NASA NTRS1984

Yaw Attitude Estimation for the Tracking and Data Relay Satellite System

The Tracking and Data Relay Satellite System (TDRSS) uses a groundbased attitude determination algorithm to open loop point the satellite's high data rate antennas. The spacecraft is able to measure its pitch and roll attitude, but its yaw attitude is periodically unobservable. The ground software uses a state-space estimator, an adaptation of a Luenberger observer, to predict the spacecraft yaw angle during these unobservable periods. It contains states associated with the roll/yaw dynamics and the on-board control law. The accuracy is limited by the modeling fidelity of the disturbance torques acting on the spacecraft. After initial operating problems were cleared up, the operation of the estimator has converged to predicted performance.

Staich, S.↗
NASA NTRS1986

Missing matter in the vicinity of the sun

The Poisson and Vlasov equations are solved numerically for realistic Galaxy models which include multiple disk components, a Population II spheroid, and an unseen massive halo. The total amount of matter in the vicinity of the sun is determined by comparing the observed distributions of tracer stars, samples of F dwarfs, and K giants with the predictions of the Galaxy models. Results are obtained for a number of different assumed distributions of the unseen disk mass. For all the observed samples, typical models imply that about half of the mass in the solar vicinity must be in the form of unobserved matter. The volume density of unobserved material near the sun is about 0.1 solar mass/cu pc; the corresponding column density is about 30 solar mass/sq pc. This so far unseen material must be in a disk with an exponential scale height of less than 0.7 kpc.

Bahcall, John N.↗
NASA NTRS1986

Dark matter near the sun

The amount of dark matter in the disk of the Galaxy at the solar position is determined by comparing the observed distributions of tracer stars with the predictions obtained from different assumptions of how the unseen matter is distributed. The major uncertainties, observational and theoretical, are estimated. For all the observed samples, typical models imply that about half of the mass in the solar vicinity must be in the form of unobserved matter. The volume density of unobserved material near the sun is about 0.1 solar mass/cu pc; the corresponding column density is about 30 solar masses/cu pc. This, so far unseen, material must be in a disk with an exponential scale height of less than 0.7 kpc. All the existing observations are consistent with the unseen disk material being in the form of stars not massive enough to burn hydrogen. It is suggested that the unseen material that is required to hold up the rotation curves of galaxies and to satisfy the virial theorem for clusters of galaxies might also be in the form of low-mass stars.

Bahcall, J. N.↗
NASA NTRS1993

Mars Operational Environmental Satellite (MOES): A post-Mars Observer discovery mission

Mars Operational Environmental Satellite (MOES) is a Discovery concept mission that is designed to observe the global short-term weather phenomena on Mars in a systematic fashion. Even after the Mariner, Viking, and, soon, Mars Observer missions, crucial aspects of the martian atmosphere will remain unobserved systematically. Achieving a better understanding of the cycles of dust, water vapor, and ices on Mars requires detailed information about atmospheric transports of those quantities associated with the weather systems, particularly those arising in mid latitudes during fall and winter. It also requires a quantitive understanding of the processes responsible for the onset and evolution of dust storms on all scales. Whereas on Earth the system of geosynchronous and polar orbiting satellites provides continuous coverage of the weather systems, on Mars the time history of important events such as regional and global dust storms remains unobserved. To understand the transport of tracers in the martian atmosphere and particularly to identify their sources and sinks, it is necessary to have systematic global, synoptic observations that have yet to be attained. Clearly these requirements are not easy to achieve from a single spacecraft in orbit, but if we focus on specific regions of the planet, e.g., polar vs. low and mid latitudes, then it is possible to attain a nearly ideal coverage at a reasonable spatial and temporal resolution with a system of just two satellites. Mars Observer is about to yield good coverage of the polar latitudes, so we focus initially on the region not covered well in terms of diurnal coverage, and in terms of desired observations will provide the initial data for the numerical models of the martian weather and climate that can be verified only with better temporal and spatial data.

Limaye, Sanjay S.↗
NASA NTRS2008

High-Precision Narrow Angle Astrometry with a Space-Borne Interferometer

This paper develops an observing and processing scheme for narrow angle astrometry using a single baseline interferometer without the aid of "grid" stars to characterize the interferometer baseline vector in inertial space. The basic concept derives from the recognition that over a narrow field the set of fundamental unknown instrument parameters that arise because the interferometer baseline vector has large uncertainties (since there are no grid star measurements) is indistinguishable from a particular set of unobservable errors in the determination of star positions within the field. Reference stars within the narrow field of regard are used to circumvent the unobservable modes. Feasibility of the approach is demonstrated through analysis and example simulations.

astrometry↗
NASA NTRS1972

The effect of multiple encounters on short period comet orbits

The observed orbital elements of short period comets are found to be consistent with the hypothesis of derivation from long period comets as long as two assumptions are made. First, the distribution of short period comets has been randomized by multiple encounters with Jupiter and second, the short period comets have lower velocities of encounter with Jupiter than is generally expected. Some 16% of the observed short period comets have lower encounter velocities than is allowed mathematically using Laplace's method. This may be due to double encounter processes with Jupiter and Saturn, or as a result of prolonged encounters. The distribution of unobservable short period comets can be inferred in part from the observed comets. Many have orbits between Jupiter and Saturn with somewhat higher inclinations than those with perihelions near the earth. Debris from those comets may form the major component of the zodiacal dust.

Lowrey, B. E.↗
NASA NTRS1971

Photochemistry of interstellar molecules

The photochemistry of two diatomic and eight polyatomic molecules is discussed quantitatively. For an interstellar molecule, the lifetime against photodecomposition depends upon the absorption cross section, the quantum yield or probability of dissociation following photon absorption, and the interstellar radiation field. The constant energy density of Habing is used for the unobserved regions of interstellar radiation field, and the field in obscuring clouds is estimated by combining the constant flux with the observed interstellar extinction curve covering the visible and ultraviolet regions. Lifetimes against photodecomposition in the unobscured regions and as a function of increasing optical thickness in obscuring clouds are calculated for the ten species. The results show that, except for CO, all the molecules have comparable lifetimes of less than one hundred years. Thus they can exist only in dense clouds and can never have been exposed to the unobscured radiation. The calculations further show that the lifetimes in clouds of moderate opacity are of the order of one million years.

Stief, L. J.↗
NASA NTRS1972

Photographic observations of the occultation of Beta Scorpii by Jupiter

The occultation of the multiple star Beta Scorpii by Jupiter was observed visually and photographically from the Bosscha Observatory in Lembang (Java), Indonesia, on May 13, 1971. The photographs recorded the dimming of the stars as the light was differentially refracted by the Jovian atmosphere, and gave support to a scale height greater than 8 km. Measurement of the position of the brightest component at Beta Scorpii during ingress shown refraction of approximately 1.4 sec before becoming unobservable.

Larson, S. M.↗