Learning to Estimate Without Bias

The Gauss Markov theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non-linear settings via deep learning with bias constraints. The classical approach to designing non-linear MVUEs is through maximum likelihood estimation (MLE) which often involves real-time computationally challenging optimizations. On the other hand, deep learning methods allow for non-linear estimators with fixed computational complexity. Learning based estimators perform optimally on average with respect to their training set but may suffer from significant bias in other parameters. To avoid this, we propose to add a simple bias constraint to the loss function, resulting in an estimator we refer to as Bias Constrained Estimator (BCE). We prove that this yields asymptotic MVUEs that behave similarly to the classical MLEs and asymptotically attain the Cramer Rao bound. We demonstrate the advantages of our approach in the context of signal to noise ratio estimation as well as covariance estimation. A second motivation to BCE is in applications where multiple estimates of the same unknown are averaged for improved performance. Examples include distributed sensor networks and data augmentation in test-time. In such applications, we show that BCE leads to asymptotically consistent estimators

Eigenvalue Distributions for a Class of Covariance Matrices with Applications to Bienenstock-Cooper-Munro Neurons Under Noisy Conditions

We analyze the effects of noise correlations in the input to, or among, BCM neurons using the Wigner semicircular law to construct random, positive-definite symmetric correlation matrices and compute their eigenvalue distributions. In the finite dimensional case, we compare our analytic results with numerical simulations and show the effects of correlations on the lifetimes of synaptic strengths in various visual environments. These correlations can be due either to correlations in the noise from the input LGN neurons, or correlations in the variability of lateral connections in a network of neurons. In particular, we find that for fixed dimensionality, a large noise variance can give rise to long lifetimes of synaptic strengths. This may be of physiological significance.Comment: 7 pages, 7 figure

Bostonia

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A simple rule for axon outgrowth and synaptic competition generates realistic connection lengths and filling fractions

Neural connectivity at the cellular and mesoscopic level appears very specific and is presumed to arise from highly specific developmental mechanisms. However, there are general shared features of connectivity in systems as different as the networks formed by individual neurons in Caenorhabditis elegans or in rat visual cortex and the mesoscopic circuitry of cortical areas in the mouse, macaque, and human brain. In all these systems, connection length distributions have very similar shapes, with an initial large peak and a long flat tail representing the admixture of long-distance connections to mostly short-distance connections. Furthermore, not all potentially possible synapses are formed, and only a fraction of axons (called filling fraction) establish synapses with spatially neighboring neurons. We explored what aspects of these connectivity patterns can be explained simply by random axonal outgrowth. We found that random axonal growth away from the soma can already reproduce the known distance distribution of connections. We also observed that experimentally observed filling fractions can be generated by competition for available space at the target neurons--a model markedly different from previous explanations. These findings may serve as a baseline model for the development of connectivity that can be further refined by more specific mechanisms.Comment: 31 pages (incl. supplementary information); Cerebral Cortex Advance Access published online on May 12, 200

Piroplasms in brown hyaenas (Parahyaena brunnea) and spotted hyaenas (Crocuta crocuta) in Namibia and South Africa are closely related to Babesia lengau

The objective of our study was identification and molecular characterisation of piroplasms and rickettsias occurring in brown (Parahyaena brunnea) and spotted hyaenas (Crocuta crocuta) from various localities in Namibia and South Africa. Whole blood (n=59) and skin (n=3) specimens from brown (n=15) and spotted hyaenas (n=47) were screened for the presence of Babesia, Theileria, Ehrlichia and Anaplasma species using the Reverse Line Blot (RLB) hybridization technique. PCR products of 52/62 (83.9%) of the specimens hybridized only with the Theileria/Babesia genus-specific probes and not with any of the species-specific probes, suggesting the presence of a novel species or variant of a species. No Ehrlichia and/or Anaplasma species DNA could be detected. Parasite 18S rRNA gene of brown (n=3) and spotted hyaena (n=6) specimens was subsequently amplified, cloned and the recombinants sequenced. Homologous sequence searches of databases indicated that the obtained sequences were most closely related to B. lengau, originally described from cheetahs (Acinonyx jubatus). Observed sequence similarities were subsequently confirmed by phylogenetic analyses which showed that the obtained hyaena sequences formed a monophyletic group with B. lengau, B. conradae and sequences previously isolated from humans and wildlife in the western USA. Within the B. lengau clade, the obtained sequences and the published B. lengau sequences grouped into six distinct groups, of which groups I to V represented novel B. lengau genotypes and/or gene variants. We suggest that these genotypes cannot be classified as new Babesia species, but rather as variants of B. lengau. This is the first report of occurrence of piroplasms in brown hyaenas.http://link.springer.com/journal/4362018-02-28hb2017Centre for Veterinary Wildlife StudiesVeterinary Tropical Disease

Significant variability exists in preoperative planning software measures of glenoid morphology for shoulder arthroplasty

Background & Hypothesis: We sought to assess the reliability of 4 different shoulder arthroplasty 3-dimensional preoperative planning programs. Comparison was also made to manual measurements conducted by 2 fellowship-trained musculoskeletal radiologists. We hypothesized that there would be significant variation in measurements of glenoid anatomy affected by glenoid deformity. Methods: A retrospective review of computed tomography (CT) scans of patients undergoing shoulder arthroplasty was undertaken. A total of 76 computed tomographies were analyzed for glenoid version and inclination by 4 templating software systems (VIP, Blueprint, TrueSight, ExactechGPS). Inter-rater reliability was assessed via intra-class correlation coefficient (ICC). For those shoulders with glenohumeral arthritis (58/76), ICC was also calculated when sub-grouping by modified Walch classification. Lin\u27s concordance correlation coefficient was calculated for each system with 2 musculoskeletal-trained radiologists’ measurements. Results: Measurements of glenoid version and inclination differed between at least 2 programs by 5º-10º in 75% and 92% of glenoids respectively, and by \u3e10º in 18% and 45% respectively. ICC was excellent for version but only moderate for inclination. ICC was highest among Walch A glenoids for both version (near excellent) and inclination (good), and lowest among Walch D for version (near poor) and Walch B for inclination (moderate). When measuring version, VIP had the highest concordance with manual measurement; Blueprint had the lowest. For inclination Blueprint had the highest concordance; ExactechGPS had the lowest. Discussion & Conclusion: Despite overall high reliability for measures of glenoid version between 4 frequently utilized shoulder arthroplasty templating softwares, this reliability is significantly affected by glenoid deformity. The programs were overall less reliable when measuring inclination, and a similar trend of decreasing reliability with increasing glenoid deformity emerged that was not statistically significant. Concordance with manual measurement is also variable. Further research is needed to understand how this variability should be accounted for during shoulder arthroplasty preoperative planning. Level of Evidence: Level III; Retrospective Comparative Stud