Variational Dropout and the Local Reparameterization Trick

We investigate a local reparameterizaton technique for greatly reducing the variance of stochastic gradients for variational Bayesian inference (SGVB) of a posterior over model parameters, while retaining parallelizability. This local reparameterization translates uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such parameterizations can be trivially parallelized and have variance that is inversely proportional to the minibatch size, generally leading to much faster convergence. Additionally, we explore a connection with dropout: Gaussian dropout objectives correspond to SGVB with local reparameterization, a scale-invariant prior and proportionally fixed posterior variance. Our method allows inference of more flexibly parameterized posteriors; specifically, we propose variational dropout, a generalization of Gaussian dropout where the dropout rates are learned, often leading to better models. The method is demonstrated through several experiments

Specificity and Kinetics of Haloalkane Dehalogenase

Haloalkane dehalogenase converts halogenated alkanes to their corresponding alcohols. The active site is buried inside the protein and lined with hydrophobic residues. The reaction proceeds via a covalent substrate-enzyme complex. This paper describes a steady-state and pre-steady-state kinetic analysis of the conversion of a number of substrates of the dehalogenase. The kinetic mechanism for the “natural” substrate 1,2-dichloroethane and for the brominated analog and nematocide 1,2-dibromoethane are given. In general, brominated substrates had a lower Km, but a similar kcat than the chlorinated analogs. The rate of C-Br bond cleavage was higher than the rate of C-Cl bond cleavage, which is in agreement with the leaving group abilities of these halogens. The lower Km for brominated compounds therefore originates both from the higher rate of C-Br bond cleavage and from a lower Ks for bromo-compounds. However, the rate-determining step in the conversion (kcat) of 1,2-dibromoethane and 1,2-dichloroethane was found to be release of the charged halide ion out of the active site cavity, explaining the different Km but similar kcat values for these compounds. The study provides a basis for the analysis of rate-determining steps in the hydrolysis of various environmentally important substrates.

Influence of mutations of Val226 on the catalytic rate of haloalkane dehalogenase

Haloalkane dehalogenase converts haloalkanes to their corresponding alcohols. The 3D structure, reaction mechanism and kinetic mechanism have been studied. The steady state kcat with 1,2-dichloroethane and 1,2-dibromoethane is limited mainly by the rate of release of the halide ion from the buried active-site cavity. During catalysis, the halogen that is cleaved off (Clα) from 1,2-dichloroethane interacts with Trp125 and the Clβ interacts with Phe172. Both these residues have van der Waals contacts with Val226. To establish the effect of these interactions on catalysis, and in an attempt to change enzyme activity without directly mutating residues involved in catalysis, we mutated Val226 to Gly, Ala and Leu. The Val226Ala and Val226Leu mutants had a 2.5-fold higher catalytic rate for 1,2-dibromoethane than the wild-type enzyme. A pre-steady state kinetic analysis of the Val226Ala mutant enzyme showed that the increase in kcat could be attributed to an increase in the rate of a conformational change that precedes halide release, causing a faster overall rate of halide dissociation. The kcat for 1,2-dichloroethane conversion was not elevated, although the rate of chloride release was also faster than in the wild-type enzyme. This was caused by a 3-fold decrease in the rate of formation of the alkyl-enzyme intermediate for 1,2-dichloroethane. Val226 seems to contribute to leaving group (Clα or Brα) stabilization via Trp125, and can influence halide release and substrate binding via an interaction with Phe172. These studies indicate that wild-type haloalkane dehalogenase is optimized for 1,2-dichloroethane, although 1,2-dibromoethane is a better substrate.

The early Pliocene Titiokura Formation: stratigraphy of a thick, mixed carbonate-siliciclastic shelf succession in Hawke's Bay Basin, New Zealand

This paper presents a systematic stratigraphic description of the architecture of the early Pliocene Titiokura Formation (emended) in the Te Waka and Maungaharuru Ranges of western Hawke's Bay, and presents a facies, sequence stratigraphic, and paleoenvironmental analysis of the sedimentary succession. The Titiokura Formation is of early Pliocene (Opoitian-Waipipian) age, and unconformably overlies Mokonui Formation, which is a regressive late Miocene and early Pliocene (Kapitean to early Opoitian) succession. In the Te Waka Range and the southern parts of the Maungaharuru Range, the Titiokura Formation comprises a single limestone sheet 20-50 m thick, with calcareous sandstone parts. In the vicinity of Taraponui Trig, and to the northeast, the results of 1:50 000 mapping show that the limestone gradually partitions into five members, which thicken markedly to the northeast to total thicknesses of c. 730 m, and concomitantly become dominated by siliciclastic sandstone. The members (all new) from lower to upper are: Naumai Member, Te Rangi Member, Taraponui Member, Bellbird Bush Member, and Opouahi Member. The lower four members are inferred to each comprise an obliquity-controlled 41 000 yr 6th order sequence, and the Opouahi Member at least two such sequences. The sequences typically have the following architectural elements from bottom to top: disconformable sequence boundary that formed as a transgressive surface of erosion; thin transgressive systems tracts (TSTs) with onlap and backlap shellbeds, or alternatively, a single compound shellbed; downlap surface; and very thick (70-200 m) highstand (HST) and regressive systems tracts (RST) composed of fine sandstone. The sequences in the Opouahi Member have cryptic TSTs, sandy siltstone to silty sandstone HSTs, and cross-bedded, differentially cemented, fine sandstone RSTs; a separate variant is an 11 m thick bioclastic limestone (grainstone and packstone) at the top of the member that crops out in the vicinity of Lake Opouahi. Lithostratigraphic correlations along the crest of the ranges suggest that the Titiokura Formation, and its correlatives to the south around Puketitiri, represent a shoreline-to-shelf linked depositional system. Carbonate production was focused around a rocky seascape as the system onlapped basement in the south, with dispersal and deposition of the comminuted carbonate on an inner shelf to the north, which was devoid of siliciclastic sediment input. The rates of both subsidence and siliciclastic sediment flux increased rapidly to the northeast of the carbonate "platform", with active progradation and offlap of the depositional system into more axial parts of Hawke's Bay Basin

Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations

Post-hoc explanations of machine learning models are crucial for people to understand and act on algorithmic predictions. An intriguing class of explanations is through counterfactuals, hypothetical examples that show people how to obtain a different prediction. We posit that effective counterfactual explanations should satisfy two properties: feasibility of the counterfactual actions given user context and constraints, and diversity among the counterfactuals presented. To this end, we propose a framework for generating and evaluating a diverse set of counterfactual explanations based on determinantal point processes. To evaluate the actionability of counterfactuals, we provide metrics that enable comparison of counterfactual-based methods to other local explanation methods. We further address necessary tradeoffs and point to causal implications in optimizing for counterfactuals. Our experiments on four real-world datasets show that our framework can generate a set of counterfactuals that are diverse and well approximate local decision boundaries, outperforming prior approaches to generating diverse counterfactuals. We provide an implementation of the framework at https://github.com/microsoft/DiCE.Comment: 13 page