Sequential Subset Research Articles

Proof of a Key Inequality for Lattice Event Probabilities with Equal Odds

Levin and Leu (2021) introduced some key inequalities that underlie the lower bound formula for the probability of lattice events when using adaptive members of the Levin-Robbins-Leu family of sequential subset selection procedures for binary outcomes. Here we provide a rigorous proof of the key inequality for each adaptive procedure in the special case of equal odds parameters. We also provide some further insight into why the key inequality holds for arbitrary odds parameters and we present a complete proof in that case for a simple yet non-trivial prototype example. Two errata in the abovementioned publication are also corrected herein.

A key inequality for lower bound formulas for lattice event probabilities

We introduce and discuss some key inequalities that underlie the lower bound formula for the probability of lattice events in the Levin-Robbins-Leu family of sequential subset selection procedures for binary outcomes. The present work combines the notion of lattice events—as previously discussed for the nonadaptive member of the family—with the positive cumulative sum property for the adaptive members—as previously discussed for the special lattice event of correct selection, thereby extending the key inequality to its broadest scope.

Modular, compositional, and executable formal semantics for LLVM IR

This paper presents a novel formal semantics, mechanized in Coq, for a large, sequential subset of the LLVM IR. In contrast to previous approaches, which use relationally-specified operational semantics, this new semantics is based on monadic interpretation of interaction trees, a structure that provides a more compositional approach to defining language semantics while retaining the ability to extract an executable interpreter. Our semantics handles many of the LLVM IR's non-trivial language features and is constructed modularly in terms of event handlers, including those that deal with nondeterminism in the specification. We show how this semantics admits compositional reasoning principles derived from the interaction trees equational theory of weak bisimulation, which we extend here to better deal with nondeterminism, and we use them to prove that the extracted reference interpreter faithfully refines the semantic model. We validate the correctness of the semantics by evaluating it on unit tests and LLVM IR programs generated by HELIX.

Positivity of cumulative sums for multi-index function components explains the lower bound formula in the Levin-Robbins-Leu family of sequential subset selection procedures

We exhibit some strong positivity properties of a certain function that implies a key inequality that in turn implies the lower bound formula for the probability of correct selection in the Levin-Robbins-Leu family of sequential subset selection procedures for binary outcomes. These properties provide a more direct and comprehensive demonstration of the key inequality than was discussed in Levin and Leu (2013a).

Adaptive sequential selection procedures with random subset sizes

ABSTRACTWe introduce a new family of sequential selection procedures wherein the subsets selected have random sizes. In comparison to subset selection procedures that select subsets of fixed size, the new procedures alleviate the need to specify the subset size prior to the experiment. We discuss the application of such procedures in the context of early phase clinical trials. The new procedures retain the adaptive features of the Levin-Robbins-Leu family of sequential subset selection procedures for selecting subsets of fixed size, namely, sequential elimination of inferior treatments and sequential recruitment of superior treatments. These two adaptive features respectively address ethical concerns that diminish interest in nonadaptive procedures and also allow promising treatments to be brought forward for further testing without having to wait until the end of the trial. The new procedures differ from the classical subset selection procedures of Shanti S. Gupta in terms of their respective goals and operating characteristics and we compare the two approaches in a simulation study. The findings suggest that whereas Gupta’s procedure achieves its goal of including the single best treatment in the final selected subset with high probability, it does so by virtue of a nonadaptive, fixed sample size procedure that lacks necessary flexibility in the context of clinical research. By contrast, the new procedures aim to select treatment subsets that satisfy a different criterion, that of acceptable subset selection with high probability, while allowing adaptive elimination and recruitment and other flexibilities which we discuss to fit the practical needs of selection methods in clinical research.

On lattice event probabilities for Levin-Robbins-Leu subset selection procedures

ABSTRACTThe Levin-Robbins-Leu (LRL) family of sequential subset selectionprocedures admits of a simple formula that provides a lower bound for the probability of various types of subset selection events. Here we demonstrate that a corresponding lower bound formula holds for lattice events when using the nonadaptive family member with binary outcomes. Lattice events are more general than the type of events that we previously considered in demonstrating that the nonadaptive LRL procedure selects “acceptable” subsets with an arbitrarily large prespecified probability irrespective of the true population parameters. Interestingly, the proof of the lower bound formula for lattice events that we present here simplifies the methods previously used and sheds additional light on why the lower bound formula holds. As for acceptable subset selection, we conjecture that the other LRL family members, which allow for adaptive elimination of inferior candidates and/or recruitment of superior candidates, obey the same lower bound formulas for lattice events.

Reasoning about the POSIX file system: local update and global pathnames

We introduce a program logic for specifying a core sequential subset of the POSIX file system and for reasoning abstractly about client programs working with the file system. The challenge is to reason about the combination of local directory update and global pathname traversal (including '..' and symbolic links) which may overlap the directories being updated. Existing reasoning techniques are either based on first-order logic and do not scale, or on separation logic and can only handle linear pathnames (no '..' or symbolic links). We introduce fusion logic for reasoning about local update and global pathname traversal, introducing a novel effect frame rule to propagate the effect of a local update on overlapping pathnames. We apply our reasoning to the standard recursive remove utility (rm -r), discovering bugs in well-known implementations.

A multi-tier semantics for Hop

Hop is a multi-tier programming language where the behavior of interacting servers and clients are expressed by a single program. Hop adheres to the standard web programming style where servers elaborate HTML pages containing JavaScript code. This JavaScript code responds locally to user's interactions but also (following the so-called Ajax style) requests services from remote servers. These services bring back new HTML fragments containing additional JavaScript code replacing or modifying the state of the client. This paper presents a continuation-based denotational semantics for a sequential subset of Hop. Though restricted to a single server and a single client, this semantics takes into account the key feature of Hop namely that the server elaborates client code to be run in the client's browser. This new client-code dynamically requests services from the server which, again, elaborate new client code to be run in the client's browser. This semantics details the programming model advocated by Hop and provides a sound basis for future studies such as security of web applications and web continuations.

An algebraic approach to the design of compilers for object-oriented languages

Abstract In this paper we describe an algebraic approach to construct provably correct compilers for object-oriented languages; this is illustrated for programs written in a language similar to a sequential subset of Java. It includes recursive classes, inheritance, dynamic binding, recursion, type casts and test, assignment, and class-based visibility, but a copy semantics. In our approach, we tackle the problem of compiler correctness by reducing the task of compilation to that of program refinement. Compilation is identified with the reduction of a source program to a normal form that models the execution of object code. The normal form is generated by a series of correctness-preserving transformations that are proved sound from the basic laws of the language; therefore it is correct by construction. The main advantages of our approach are the characterisation of compilation within a uniform framework, where comparisons and translations between semantics are avoided, and the modularity and extensibility of the resulting compiler.

Integration of Soft Computing Approaches for Feature Subset Selection

Feature subset selection basically depends on the design of a criterion function to measure the effectiveness of a particular feature or a feature subset and the selection of a search strategy to find out he best feature subset. Lots of techniques, mostly statistical, have been developed so far which are mainly categorized into classifier independent filter approaches and classifier dependant wrapper approaches. Wrapper approaches produce good results but are computationally unattractive specially when nonlinear neural classifiers with complex learning algorithms are used The present work proposes some hybrid algorithms for feature subset selection using individual tools from soft computing paradigm taking advantage of both the filter and wrapper approaches. Artificial neural network, fuzzy logic and genetic algorithm are used to design neuro fuzzy and fuzzy genetic algorithms. A fuzzy set theoretic measure for assessing the goodness of a feature is used in conjunction with a multilayer perceptron (MLP) or a fractal neural network (FNN), the proposed modification of MLP having a statistically fractal sparse architecture. Though the process does not guarantee absolute optimality, the selected feature subset produces near optimal results for practical purposes. The process is less time consuming and computationally light compared to any neural network classifier based sequential feature subset selection technique. The same measure in conjunction with genetic algorithm has been used and it is found that fuzzy genetic algorithm is better than neuro fuzzy algorithms for large feature set problems for finding out a near optimal solution. The proposed algorithms have been simulated with two different data sets to show their effectiveness.

On a sequential subset selection procedure for the least probable multinomial cell

This paper studies a sequential procedure R for selecting a random size subset that contains the multinomial cell which has the smallest cell probability. The stopping rule of the proposed procedure R is the composite of the stopping rules of curtailed sampling, inverse sampling, and the Ramey-Alam sampling. A reslut on the worst configuration is shown and it is employed in computing the procedure parameters that guarantee certain probability requirements. Tables of these procedure parameters, the corresponding probability of correct selection, the expected sample size, and the expected subset size are given for comparison purpose.

Rapid Sequential Processing in Dyslexic and Ordinary Readers

42 dyslexic and 42 ordinary readers were given a rapid sequential short-term memory task using materials adapted from the Illinois Test of Psycholinguistic Abilities Visual Sequential Memory subset. Dyslexic readers performed at a similar level to ordinary readers. In Study 2, the same readers were given a 10-piece form board to complete as quickly as possible. Dyslexic readers were significantly slower on this task. Since short-term memory was not a feature of the second task, it was reasoned that short-term memory problems were unlikely to be a feature of dyslexic's performances on rapid sequential processing tasks.