We propose an approach to rapidly find the upper limit of separability between datasets that is directly applicable to HEP classification problems. The most common HEP classification task is to use n values (variables) for an object (event) to estimate the probability that it is signal vs. background. Most techniques first use known samples to identify differences in how signal and background events are distributed throughout the n-dimensional variable space, then use those differences to classify events of unknown type. Qualitatively, the greater the differences, the more effectively one can classify events of unknown type. We will show that the Mutual Information (MI) between the n-dimensional signal-background mixed distribution and the answers for the known events, tells us the upper-limit of separation for that set of n variables. We will then compare that value to the Jensen-Shannon Divergence between the output distributions from a classifier to test whether it has extracted all possible information from the input variables. We will also discuss speed improvements to a standard method for calculating MI.Our approach will allow one to: a) quickly measure the maximum possible effectiveness of a large number of potential discriminating variables independent of any specific classification algorithm, b) identify potential discriminating variables that are redundant, and c) determine whether a classification algorithm has achieved the maximum possible separation. We test these claims first on simple distributions and then on Monte Carlo samples generated for Supersymmetry and Higgs searches. In all cases, we were able to a) predict the separation that a classification algorithm would reach, b) identify variables that carried no additional discriminating power, and c) identify whether an algorithm had reached the optimum separation. Our code is publicly available.
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In the Entropic Dynamics framework the dynamics is driven by maximizing entropy subject to appropriate constraints. In this work we bring Entropic Dynamics one step closer to full equivalence with quantum theory by identifying constraints that lead to wave functions that remain single-valued even for multi-valued phases by recognizing the intimate relation between quantum phases, gauge symmetry, and charge quantization.
Background: Self-injection of biologics is a mainstay of chronic disease treatment, yet the process of self-injection often causes persistent apprehension and anxiety, distinct from needle phobia. While literature alludes to the role that routines and rituals play in self-injection, there is no comprehensive study on the routines and rituals self-injectors employ, nor of the process by which they are discovered and ingrained. Methods: We conducted a mixed-method, observational pilot ethnography study of 27 patients with plaque psoriasis, psoriatic arthritis, or ankylosing spondylitis with and without prior biologic self-injection experience. Patients submitted self-made videos, photos, and projective exercises of an actual biologic self-injection and completed validated instruments to assess burden of treatment. Videos and photos containing routine and ritual elements were thematically categorized based on functional and emotional benefit, and analyzed for differences based on current biologic, dosing frequency, time on current biologic, and burden of treatment measures. Results: During patients' initial at-home injections, training gaps became apparent, leading to a process of experimentation aimed at reducing pain/anxiety, increasing confidence, and building a consistent injection process. Routines were present in 27/27 (100%) patients and anchored the time, place, and process for injection, and incorporated approved use steps for the injection device. Ritual elements served as emotional coping strategies for patients and were present in 21/27 (77.8%) of patients. Conclusion: Our findings suggest that providing patients device training using adult learning principles, teaching routines and rituals concurrently, and providing at-home opportunities for practice with a device trainer may be useful strategies to reduce anxiety, avoid unnecessary experimentation, and improve adherence to injection therapy. While further studies are needed to generalize our findings, we posit that routine and ritual elements can be incorporated into existing patient-clinician interactions or novel digital interventions through mobile medical applications, smart training devices, and connected injection ecosystems.
In this paper we focus on the estimation of mutual information from finite samples (X ×Y). The main concern with estimations of mutual information is their robustness under the class of transformations for which it remains invariant: i.e. type I (coordinate transformations), III (marginalizations) and special cases of type IV (embeddings, products). Estimators which fail to meet these standards are not robust in their general applicability. Since most machine learning tasks employ transformations which belong to the classes referenced in part I, the mutual information can tell us which transformations are most optimal [1]. There are several classes of estimation methods in the literature, such as non-parametric estimators like the one developed by Kraskov et. al [2], and its improved versions [3]. These estimators are extremely useful, since they rely only on the geometry of the underlying sample, and circumvent estimating the probability distribution itself. We explore the robustness of this family of estimators in the context of our design criteria.
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