The Computational Complexity of Understanding Binary Classifier Decisions

Non-cancellative Boolean circuits: A generalization of monotone boolean circuits

Full-chip statistical leakage power analysis typically requires quadratic time complexity in the presence of spatial correlation. When spatial correlation are strong (with large spatial correlation length), efficient linear time complexity analysis can be attained as the number of variational variables can be significantly reduced. However this is not the case for circuits where gate leakage currents are weakly correlated. In this paper, we present a linear time algorithm for statistical leakage power analysis in the presence of weak spatial correlation. The new algorithm exploits the fact that gate leakage current can be efficiently computed locally when correlation is weak. We adopt a newly proposed spatial correlation model where a new set of location-dependent uncorrelated variables are defined over virtual grids to represent the original physical random variables via fitting. To compute the leakage current of a gate on the new set of variables, the new method uses the orthogonal polynomials based collocation method, which can be applied to any gate leakage models. The total leakage currents are then computed by simply summing up the resulting orthogonal polynomials (their coefficients) on the new set of variables for all gates. Experimental results show that the proposed method is about two orders of magnitude faster than the recently proposed grid-based method [3] with similar accuracy and many orders of magnitude times over the Monte Carlo method.

Cyclic Boolean circuits

This is the first of a series of papers on the theme of automated pollen analysis. The automation of pollen analysis could result in numerous advantages for the reconstruction of past environments, with larger data sets made practical, objectivity and fine resolution sampling. There are also applications in apiculture and medicine. Previous work on the classification of pollen using texture measures has been successful with small numbers of pollen taxa. However, as the number of pollen taxa to be identified increases, more features may be required to achieve a successful classification. This paper describes the use of simple geometric measures to augment the texture measures. The feasibility of this new approach is tested using scanning electron microscope (SEM) images of 12 taxa of fresh pollen taken from reference material collected on Henderson Island, Polynesia. Pollen images were captured directly from a SEM connected to a PC. A threshold grey‐level was set and binary images were then generated. Pollen edges were then located and the boundaries were traced using a chain coding system. A number of simple geometric variables were calculated directly from the chain code of the pollen and a variable selection procedure was used to choose the optimal subset to be used for classification. The efficiency of these variables was tested using a leave‐one‐out classification procedure. The system successfully split the original 12 taxa sample into five sub‐samples containing no more than six pollen taxa each. The further subdivision of echinate pollen types was then attempted with a subset of four pollen taxa. A set of difference codes was constructed for a range of displacements along the chain code. From these difference codes probability variables were calculated. A variable selection procedure was again used to choose the optimal subset of probabilities that may be used for classification. The efficiency of these variables was again tested using a leave‐one‐out classification procedure. The proportion of correctly classified pollen ranged from 81% to 100% depending on the subset of variables used. The best set of variables had an overall classification rate averaging at about 95%. This is comparable with the classification rates from the earlier texture analysis work for other types of pollen. Copyright © 2004 John Wiley & Sons, Ltd.

A faster FPTAS for knapsack problem with cardinality constraint

Lattice-based cryptography has recently emerged as a prime candidate for efficient and secure post-quantum cryptography. The two main hard problems underlying its security are the shortest vector problem (SVP) and the closest vector problem (CVP). Various algorithms have been studied for solving these problems, and for SVP, lattice sieving currently dominates in terms of the asymptotic time complexity: one can heuristically solve SVP in time $2^{0.292d}$ in high dimensions $d$ [BDGL'16]. Although several SVP algorithms can also be used to solve CVP, it is not clear whether this also holds for heuristic lattice sieving methods. The best time complexity for CVP is currently $2^{0.377d}$ [BGJ'14]. In this paper we revisit sieving algorithms for solving SVP, and study how these algorithms can be modified to solve CVP and its variants as well. Our first method is aimed at solving one problem instance and minimizes the overall time complexity for a single CVP instance with a time complexity of $2^{0.292d}$. Our second method minimizes the amortized time complexity for several instances on the same lattice, at the cost of a larger preprocessing cost. We can solve the closest vector problem with preprocessing (CVPP) with $2^{0.636d}$ space and preprocessing, in $2^{0.136d}$ time, while the query complexity can even be reduced to $2^{\epsilon d}$ at the cost of preprocessing time and memory complexities of $(1/\epsilon)^{O(d)}$. For easier variants of CVP, such as approximate CVP and bounded distance decoding (BDD), we further show how the preprocessing method achieves even better complexities. For instance, we can solve approximate CVPP with large approximation factors $k$ with polynomial-sized advice in polynomial time if $k = \Omega(\sqrt{d/\log d})$, heuristically closing the gap between the decision-CVPP result of [AR'04] and the search-CVPP result of [DRS'14].

Let f be a function on a set of variables V. For each x e V, let c(x) be the cost of reading the value of x. An algorithm for evaluating f is a strategy for adaptively identifying and reading a set of variables U ⊆ V whose values uniquely determine the value of f. We are interested in finding algorithms which minimize the cost incurred to evaluate f in the above sense. Competitive analysis is employed to measure the performance of the algorithms. We study two variants of the above problem. First we consider the classical setting in which one assumes that the algorithm knows the cost c(x), for each x e V. For the case where f is a monotone boolean function which is representable by a threshold tree, we provide a polynomial time algorithm with the best possible competitive ratio γfc for each fixed cost function c(·). Remarkably, the best known result for the same class of functions is a pseudo-polynomial algorithm with competitiveness 2γfc. For the class of game tree functions our polynomial time algorithm attains, for each fixed cost function, the same competitiveness as the best known algorithm for the same class of functions, which instead runs in pseudo-polynomial time.In the second part of the paper, we study a novel variant of the problem. Here, we assume that the cost function is not known in advance and some preemption is allowed in the reading operations. This model has applications, e.g., when reading a variable coincides with obtaining the output of a job on a CPU and the cost is the CPU time. In such a case, it is reasonable to assume that no exact knowledge of the cost is available. We define a new algorithm for this problem based on the solution of a Linear Program. We show the optimality of our algorithm for the class of monotone boolean functions representable by AND-OR-trees. We also show a sub-optimal implementation for general monotone boolean functions.

Subsequent to the identification of a set of variables that best discriminate between two populations, there might still exist nonstatistical reasons for further exploration of a specific subset in terms of its relative discriminating ability. This requires a more f exible criterion than the usual one based on tests of equality of the Mahalanobis distances. A measure of the extent to which a set and a specific subset of variables agree in the discriminant analysis problem, under multivariate normal assumptions, is proposed. This measure is the probability of concordance in classification and its value is shown to be high when the subset of variables suggest large separation between the two populations. A justification for the use of the subset of variables can be derivedfrom a hlgh probability of concordance and the non-statistical considerations discussed in the text. In the two-population (II; i - 1, 2) discriminant analysis problem based on a p-variate normal density, the hypothesis testing techniques intended to result in possible variable reduction are presented in texts such as Kshirsagar's (1972). The methods involve the comparison of the p-variate Mahalanobis distance with that of a specific subset q(q < p). The rejection of the hypothesis of equal distances dictates the use of the p variables in the classification procedure. However, there might be nonstatistical reasons for further exploration of the subset in terms of its relative discriminating ability. For instance, in critical care medical research, the variables that best differentiate between survivors and non-survivors are often realized using both invasive and non-invasive techniques. But the invasive techniques frequently interfere with the condition of the patient (Weil and Shubin 1967). In other research areas, some variables might be prohibitively expensive to measure on a routine basis although their inclusion might increase the probabilities of correct classification. Hence, there exists a real need for a flexible criterion, based on relative discriminating ability, that can be used for the comparison of a set of variables with a specific subset. In this article we present a measure of the degree to which a set and a specific subset of variables agree in the classification of an individual (object) into any one of two populations.

Artificial intelligence techniques to forecasts based on the Community Multiscale Air Quality (PM2.5) operational model can be known using TensorFlow. TensorFlow was used in this study to assess the scores of the Recurrent Neural Networks (RNN) input variables on the 6-hour forecast for July-October 2022. The relevance scores for the one- and two-day forecasts are represented by the sum of the relevance scores across the target prediction timeframe 2–5 and 4–7 previous time steps. The initial selection of input variables was based on their correlation coefficient with the measured PM2.5 concentration. Still, the order of contribution of the input variables measured by TensorFlow was different from the order of their correlation coefficients, which indicated an inconsistency between the linear and nonlinear variables of the method. It was found that the retraining of the RNN model using a subset of variables with a high relevance score resulted in a predictive ability similar to the initial set of input variables.

Most successful object recognition systems rely on binary classification, deciding only if an object is present or not, but not providing information on the actual object location. To perform localization, one can take a sliding window approach, but this strongly increases the computational cost, because the classifier function has to be evaluated over a large set of candidate subwindows. In this paper, we propose a simple yet powerful branch-and-bound scheme that allows efficient maximization of a large class of classifier functions over all possible subimages. It converges to a globally optimal solution typically in sublinear time. We show how our method is applicable to different object detection and retrieval scenarios. The achieved speedup allows the use of classifiers for localization that formerly were considered too slow for this task, such as SVMs with a spatial pyramid kernel or nearest neighbor classifiers based on the chi2-distance. We demonstrate state-of-the-art performance of the resulting systems on the UIUC Cars dataset, the PASCAL VOC 2006 dataset and in the PASCAL VOC 2007 competition.

Binary classification of floor vibrations for human activity detection based on dynamic mode decomposition

The number of Internet of Things (IoT) devices connected to the network enlarges dramatically these days. This leads to rising cyberattacks, such as botnets. These attacks result in disrupting the transition of networks and services for IoT devices. Recently, various approaches of Machine Learning (ML) and Deep Learning (DL) have been proposed to detect botnet attacks in the IoT environment. However, the ML/DL methods used in the research are just binary classification between normal and attack classes. In this study, we propose an approach using ML algorithms to develop multi-classification botnet detection systems for IoT devices. The proposed approach is based on not only multi-classification metrics but also the time complexity of the training and testing processes. The multi-classification metrics, particularly multi- classification confusion matrix, Accuracy, Macro F1-score, Micro F1-score, Weighted F1-score, Mathews Correlation Coefficient (MCC), and Cohen Kappa score are used in the entire study. Through the extensive experiments with the N-BaIoT dataset, the Artificial Neural Network classifier has proven its robust performance in terms of both multi-classification metrics and time complexity.

We consider the classic scheduling problem of minimizing the total weighted flow-time on a single machine (min-WPFT), when preemption is allowed. In this problem, we are given a set of $n$ jobs, each job having a release time $r_j$, a processing time $p_j$, and a weight $w_j$. The flow-time of a job is defined as the amount of time the job spends in the system before it completes; that is, $F_j = C_j - r_j$, where $C_j$ is the completion time of job. The objective is to minimize the total weighted flow-time of jobs. This NP-hard problem has been studied quite extensively for decades. In a recent breakthrough, Batra, Garg, and Kumar presented a {\em pseudo-polynomial} time algorithm that has an $O(1)$ approximation ratio. The design of a truly polynomial time algorithm, however, remained an open problem. In this paper, we show a transformation from pseudo-polynomial time algorithms to polynomial time algorithms in the context of min-WPFT. Our result combined with the result of Batra, Garg, and Kumar settles the long standing conjecture that there is a polynomial time algorithm with $O(1)$-approximation for min-WPFT.

Blood cardioplegia can be administered both in anterograde and retrograde fashions. In an effort to better define the clinical performance of the combined anterograde/retrograde cardioplegia, this work compares the results yielded by this method with those obtained with the classic asanguineous crystalloid cardioplegia by analyzing their effects on a set of physiological variables monitored in patients. A set of 96 adult patients monitored in the intensive care unit (ICU) after hypothermic cardiopulmonary bypass for coronary or valvular disease was studied. In 55 patients the crystalloid cardioplegia technique was used as hypothermic treatment, while in the other patients the antero/retrograde blood cardioplegic technique was adopted. The statistical analysis developed can be divided into two phases. The first analyzes the separability of the two classes and their evolution in time. The second phase deals with the problem of identifying the single variable and/or the variable subset with the greatest separation power. The results confirm the role of the antero/retrograde blood cardioplegia in myocardium protection. >

Various methods have been proposed to identify emergent dynamical structures in complex systems. In this paper, we focus on the Dynamical Cluster Index (DCI), a measure based on information theory which allows one to detect relevant sets, i.e. sets of variables that behave in a coherent and coordinated way while loosely interacting with the rest of the system. The method associates a score to each subset of system variables; therefore, for a thorough analysis of the system, it requires an exhaustive enumeration of all possible subsets. For large systems, the curse of dimensionality makes the problem solvable only using metaheuristics. Even within such approaches, however, DCI computation has to be performed for a huge number of times; thus, an efficient implementation becomes a mandatory requirement. Considering that a candidate relevant set’s DCI can be computed independently of the others, we propose a GPU-based massively parallel implementation of DCI computation. We describe the algorithm’s structure and validate it by assessing the speedup in comparison with a single-thread sequential CPU implementation when analyzing a set of dynamical systems of different sizes.