Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low dimensional projection can help alleviate this curse of dimensionality, but introduces many trainable hyperparameters, which can be cumbersome, especially in the small data regime. We use additive sums of kernels for GP regression, where each kernel operates on a different random projection of its inputs. Surprisingly, we find that as the number of random projections increases, the predictive performance of this approach quickly converges to the performance of a kernel operating on the original full dimensional inputs, over a wide range of data sets, even if we are projecting into a single dimension. As a consequence, many problems can remarkably be reduced to one dimensional input spaces, without learning a transformation. We prove this convergence and its rate, and additionally propose a deterministic approach that converges more quickly than purely random projections. Moreover, we demonstrate our approach can achieve faster inference and improved predictive accuracy for high-dimensional inputs compared to kernels in the original input space.
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Local Projection Inference Is Simpler and More Robust Than You Think
Applied macroeconomists often compute confidence intervals for impulse responses using local projections, that is, direct linear regressions of future outcomes on current covariates. This paper proves that local projection inference robustly handles two issues that commonly arise in applications: highly persistent data and the estimation of impulse responses at long horizons. We consider local projections that control for lags of the variables in the regression. We show that lag‐augmented local projections with normal critical values are asymptotically valid uniformly over (i) both stationary and non‐stationary data, and also over (ii) a wide range of response horizons. Moreover, lag augmentation obviates the need to correct standard errors for serial correlation in the regression residuals. Hence, local projection inference is arguably both simpler than previously thought and more robust than standard autoregressive inference, whose validity is known to depend sensitively on the persistence of the data and on the length of the horizon.
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- Award ID(s):
- 1851665
- NSF-PAR ID:
- 10281004
- Date Published:
- Journal Name:
- Econometrica
- Volume:
- 89
- Issue:
- 4
- ISSN:
- 0012-9682
- Page Range / eLocation ID:
- 1789 to 1823
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Our ability to project changes to the climate via anthropogenic forcing has steadily increased over the last five decades. Yet, biologists still lack accurate projections about climate change impacts. Despite recent advances, biologists still often rely on correlative approaches to make projections, ignore important mechanisms, develop models with limited coordination, and lack much of the data to inform projections and test them. In contrast, atmospheric scientists have incorporated mechanistic data, established a global network of weather stations, and apply multi‐model inference by comparing divergent model projections. I address the following questions: How have the two fields developed through time? To what degree does biological projection differ from climate projection? What is needed to make similar progress in biological projection? Although the challenges in biodiversity projections are great, I highlight how biology can make substantial progress in the coming years. Most obstacles are surmountable and relate to history, lag times, scientific culture, international organization, and finances. Just as climate change projections have improved, biological modeling can improve in accuracy by incorporating mechanistic understanding, employing multi‐model ensemble approaches, coordinating efforts worldwide, and validating projections against records from a well‐designed network of biotic stations. Now that climate scientists can make better projections of climate change, biologists need to project and prevent its impacts on biodiversity.
This article is categorized under:
Climate, Ecology, and Conservation > Modeling Species and Community Interactions
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null (Ed.)We prove that local projections (LPs) and Vector Autoregressions (VARs) estimate the same impulse responses. This nonparametric result only requires unrestricted lag structures. We discuss several implications: (i) LP and VAR estimators are not conceptually separate procedures; instead, they are simply two dimension reduction techniques with common estimand but different finite‐sample properties. (ii) VAR‐based structural identification—including short‐run, long‐run, or sign restrictions—can equivalently be performed using LPs, and vice versa. (iii) Structural estimation with an instrument (proxy) can be carried out by ordering the instrument first in a recursive VAR, even under noninvertibility. (iv) Linear VARs are as robust to nonlinearities as linear LPs.more » « less
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Abstract Most earth system models fail to capture the seasonality of carbon fluxes in radiation‐limited tropical evergreen forests (TEF) in the Amazon. Kim et al. (2012,
https://doi.org/10.1111/j.1365-2486.2011.02629.x ) first statistically incorporated a light‐controlled phenology module into an ecosystem model to improve carbon flux simulations at one TEF site. However, it is not clear how their approach can be extended to other TEF sites with different climatic conditions. Here we evaluated temporal variability in plant functional traits at three different TEF sites using a data‐conditioned stochastic parameterization method. We showed that previously studied links—between seasonal photosynthetically active radiation (PAR) and the traitsV c max25and leaf longevity—occur across sites. We further determined that seasonal PAR could similarly drive variations in the stomatal conductance slope parameter. Differences found in temporal trait estimates among sites indicate that dynamic trait parameters cannot be applied uniformly over space, but it may be possible to extrapolate them based on climatic factors. Motivated by recent observations that physiological capacity develops as leaves mature, we built new regression models for predicting traits that not only include PAR but also an autoregressive lag term to capture observed physiological delays behind PAR‐driven phenology shifts. With our stochastic parameterization, we predicted the three sites to be carbon neutral or carbon sinks under the RCP 8.5 future climate scenario. In contrast, projections using standard static trait parameters show most of the Amazonian TEF region becoming a carbon source. We further approximated that variable traits may allow at least a third of the radiation‐limited TEF region in the Amazon to serve as a future net carbon sink. -
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Abstract Exertional heat illness and stroke are serious concerns across youth and college sports programs. While some teams and governing bodies have adopted the wet bulb globe temperature (WBGT), few practitioners use measurements on the field of play; rather, they often rely on regionally modeled or estimated WBGT. However, urban development-induced heat and projected climate change increase exposure to heat. We examined WBGT levels between various athletic surfaces and regional weather stations under current and projected climates and in hot-humid and hot-dry weather regimes in the southwest U.S. in Tempe, Arizona. On-site sun-exposed WBGT data across five days (07:00–19:00 local time) in June (dry) and August (humid) were collected over five athletic surfaces: rubber, artificial turf, clay, grass, and asphalt. Weather station data were used to estimate regional WBGT (via the Liljegren model) and compared to on-site, observed WBGT. Finally, projected changes to WBGT were modeled under mid-century and late-century conditions. On-field WBGT observations were, on average, significantly higher than WBGT estimated from regional weather stations by 2.4 °C–2.5 °C, with mean on-field WBGT across both months of 28.5 ± 2.76 °C (versus 25.8 ± 3.21 °C regionally). However, between-athletic surface WBGT differences were largely insignificant. Significantly higher mean WBGTs occurred in August (30.1 ± 2.35 °C) versus June (26.9 ± 2.19 °C) across all venues; August conditions reached ‘limit activity’ or ‘cancellation’ thresholds for 6–8 h and 2–4 h of the day, respectively, for all sports venues. Climate projections show increased WBGTs across measurement locations, dependent on projection and period, with average August WBGT under the highest representative concentration pathway causing all-day activity cancellations. Practitioners are encouraged to use WBGT devices within the vicinity of the fields of play, yet should not rely on regional weather station estimations without corrections used. Heat concerns are expected to increase in the future, underlining the need for athlete monitoring, local cooling design strategies, and heat adaptation for safety.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3982/ECTA18756
