Adaptive Walks Research Articles

Predictive Patterns and Market Efficiency: A Deep Learning Approach to Financial Time Series Forecasting

This study explores market efficiency and behavior by integrating key theories such as the Efficient Market Hypothesis (EMH), Adaptive Market Hypothesis (AMH), Informational Efficiency and Random Walk theory. Using LSTM enhanced by optimizers like Stochastic Gradient Descent (SGD), Adam, AdaGrad, and RMSprop, we analyze market inefficiencies in the Standard and Poor’s (SPX) index over a 22-year period. Our results reveal “pockets in time” that challenge EMH predictions, particularly with the AdaGrad optimizer at a size of the hidden layer (HS) of 64. Beyond forecasting, we apply the Dominguez–Lobato (DL) and General Spectral (GS) tests as part of the Martingale Difference Hypothesis to assess statistical inefficiencies and deviations from the Random Walk model. By emphasizing “informational efficiency”, we examine how quickly new information is reflected in stock prices. We argue that market inefficiencies are transient phenomena influenced by structural shifts and information flow, challenging the notion that forecasting alone can refute EMH. Additionally, we compare LSTM with ARIMA with Exponential Smoothing, and LightGBM to highlight the strengths and limitations of these models in financial forecasting. The LSTM model excels at capturing temporal dependencies, while LightGBM demonstrates its effectiveness in detecting non-linear relationships. Our comprehensive approach offers a nuanced understanding of market dynamics and inefficiencies.

The distribution of fitness effects during adaptive walks using a simple genetic network.

The tempo and mode of adaptation depends on the availability of beneficial alleles. Genetic interactions arising from gene networks can restrict this availability. However, the extent to which networks affect adaptation remains largely unknown. Current models of evolution consider additive genotype-phenotype relationships while often ignoring the contribution of gene interactions to phenotypic variance. In this study, we model a quantitative trait as the product of a simple gene regulatory network, the negative autoregulation motif. Using forward-time genetic simulations, we measure adaptive walks towards a phenotypic optimum in both additive and network models. A key expectation from adaptive walk theory is that the distribution of fitness effects of new beneficial mutations is exponential. We found that both models instead harbored distributions with fewer large-effect beneficial alleles than expected. The network model also had a complex and bimodal distribution of fitness effects among all mutations, with a considerable density at deleterious selection coefficients. This behavior is reminiscent of the cost of complexity, where correlations among traits constrain adaptation. Our results suggest that the interactions emerging from genetic networks can generate complex and multimodal distributions of fitness effects.

An enhanced sparrow search swarm optimizer via multi-strategies for high-dimensional optimization problems

With the development of science and technology, high-dimensional global optimization problems have become increasingly prevalent for scientific research and engineering, such as gene recognition, vehicle routing, job scheduling, and network topology. These problems are typically characterized by enormous and complex search spaces and numerous local minima, making it challenging to find the global optimal solution with limited computing resources. This paper introduces an enhanced sparrow search swarm optimizer (ESSSO) based on a bio-mimetic method. The ESSSO employs an adaptive sinusoidal walk strategy based on the von Mises distribution, a learning strategy utilizing roulette wheel selection, a two-stage evolution strategy, and a selection mutation strategy to address these issues. The proposed sinusoidal walk strategy, grounded in the von Mises distribution, supports a balanced evolutionary search. This mechanism disperses the individuals in a swarm in various directions based on a circular normal distribution. It then leads the search and adaptively adjusts their step sizes according to the size of the search domain during each generation of evolution. The learning strategy, based on roulette wheel selection, enhances the diversity of the population and improves the global search capability of the algorithm during the initial iterations. The two-stage evolution strategy involves a sine-learning mechanism based on the von Mises distribution and an adaptive mutation mechanism. The former is designed to boost the convergence speed of ESSSO, while the latter prevents ESSSO from getting trapped in a local optimum. Additionally, the selection mutation strategy further enhances convergence speed while maintaining population diversity. These strategies promote exploration in the early stages of evolution and exploitation in the later stages, enabling a well-balanced search for optimal solutions. We conducted comprehensive experiments two standard benchmark sets (i.e., CEC2010 and CEC2013), antenna array optimization, feature selection, and four engineering design problems. The results indicate that ESSSO outperforms ten comparison algorithms, especially in scenarios with smaller population sizes. This confirms its effectiveness in high-dimensional global optimization tasks and demonstrates that it can achieve better results with less computational resource consumption.

COMPARISON OF APARCH-TYPE MODELS: DOES THE CONTINUOUS AND JUMP COMPONENTS OF REALIZED VOLATILITY IMPROVE THE FITTING?

This study aims to extend an APARCH-X(1,1) model to the APARCH-CJ(1,1) by separating the exogenous variable X into two components: continuous and discontinuous (jump). The study was based on the application of models to 1-min intraday high-frequency data from the Tokyo Stock Price Index from 2004 to 2011, where its dependent variable is daily return and its exogenous variability is Realized Volatility. As a basic framework, the return errors follow a Normal distribution. An Adaptive Random Walk Metropolis (ARWM) method was constructed in the Markov Chain Monte Carlo algorithm to estimate model parameters so that the model fits the observed return time series. By visual inspection, the parameter trace plots showed good convergence of the Markov chains, indicating that the ARWM method is efficient in estimating the studied models. Based on the results of the Akaike Information Criterion for model fitting to data, this study found that APARCH-CJ(1,1) is inferior to APARCH(1,1).

Distance-Aware Learning for Inductive Link Prediction on Temporal Networks.

Inductive link prediction on temporal networks aims to predict the future links associated with node(s) unseen in the historical timestamps. Existing methods generate the predictions mainly by learning node representation from the node/edge attributes as well as the network dynamics or by measuring the distance between nodes on the temporal network structure. However, the attribute information is unavailable in many realistic applications and the structure-aware methods highly rely on nodes' common neighbors, which are difficult to accurately detect, especially in sparse temporal networks. Thus, we propose a distance-aware learning (DEAL) approach for inductive link prediction on temporal networks. Specifically, we first design an adaptive sampling method to extract temporal adaptive walks for nodes, increasing the probability of including the common neighbors between nodes. Then, we design a dual-channel distance measuring component, which simultaneously measures the distance between nodes in the embedding space and on the dynamic graph structure for predicting future inductive edges. Extensive experiments are conducted on three public temporal network datasets, i.e., MathOverflow, AskUbuntu, and StackOverflow. The experimental results validate the superiority of DEAL over the state-of-the-art baselines in terms of accuracy, area under the ROC curve (AUC), and average precision (AP), where the improvements are especially obvious in scenarios with only limited data.

Equitable Top-k Results for Long Tail Data

For datasets exhibiting long tail phenomenon, we identify a fairness concern in existing top-k algorithms, that return a "fixed" set of k results for a given query. This causes a handful of popular records (products, items, etc) getting overexposed and always be returned to the user query, whereas, there exists a long tail of niche records that may be equally desirable (have similar utility). To alleviate this, we propose θ-Equiv-top-k-MMSP inside existing top-k algorithms - instead of returning a fixed top-k set, it generates all (or many) top-k sets that are equivalent in utility and creates a probability distribution over those sets. The end user will be returned one of these sets during the query time proportional to its associated probability, such that, after many draws from many end users, each record will have as equal exposure as possible (governed by uniform selection probability). θ-Equiv-top-k-MMSP is formalized with two sub-problems. (a) θ-Equiv-top-k-Sets to produce a set S of sets, each set has k records, where the sets are equivalent in utility with the top-k set; (b) MaxMinFair to produce a probability distribution over S, that is, PDF(S), such that the records in S have uniform selection probability. We formally study the hardness of θ-Equiv-top-k-MMSP. We present multiple algorithmic results - (a) An exact solution for θ-Equiv-top-k-Sets, and MaxMinFair. (b) We design highly scalable algorithms that solve θ-Equiv-top-k-Sets through a random walk and is backed by probability theory, as well as a greedy solution designed for MaxMinFair. (c) We finally present an adaptive random walk based algorithm that solves θ-Equiv-top-k-Sets and MaxMinFair at the same time. We empirically study how θ-Equiv-top-k-MMSP can alleviate a equitable exposure concerns that group fairness suffers from. We run extensive experiments using 6 datasets and design intuitive baseline algorithms that corroborate our theoretical analysis.

Oncogenic context shapes the fitness landscape of tumor suppression

Tumors acquire alterations in oncogenes and tumor suppressor genes in an adaptive walk through the fitness landscape of tumorigenesis. However, the interactions between oncogenes and tumor suppressor genes that shape this landscape remain poorly resolved and cannot be revealed by human cancer genomics alone. Here, we use a multiplexed, autochthonous mouse platform to model and quantify the initiation and growth of more than one hundred genotypes of lung tumors across four oncogenic contexts: KRAS G12D, KRAS G12C, BRAF V600E, and EGFR L858R. We show that the fitness landscape is rugged—the effect of tumor suppressor inactivation often switches between beneficial and deleterious depending on the oncogenic context—and shows no evidence of diminishing-returns epistasis within variants of the same oncogene. These findings argue against a simple linear signaling relationship amongst these three oncogenes and imply a critical role for off-axis signaling in determining the fitness effects of inactivating tumor suppressors.

Genetic Architecture of Flowering Time Differs Between Populations With Contrasting Demographic and Selective Histories.

Understanding the evolutionary factors that impact the genetic architecture of traits is a central goal of evolutionary genetics. Here, we investigate how quantitative trait variation accumulated over time in populations that colonized a novel environment. We compare the genetic architecture of flowering time in Arabidopsis populations from the drought-prone Cape Verde Islands and their closest outgroup population from North Africa. We find that trait polygenicity is severely reduced in the island populations compared to the continental North African population. Further, trait architectures and reconstructed allelic histories best fit a model of strong directional selection in the islands in accord with a Fisher-Orr adaptive walk. Consistent with this, we find that large-effect variants that disrupt major flowering time genes (FRI and FLC) arose first, followed by smaller effect variants, including ATX2 L125F, which is associated with a 4-day reduction in flowering time. The most recently arising flowering time-associated loci are not known to be directly involved in flowering time, consistent with an omnigenic signature developing as the population approaches its trait optimum. Surprisingly, we find no effect in the natural population of EDI-Cvi-0 (CRY2 V367M), an allele for which an effect was previously validated by introgression into a Eurasian line. Instead, our results suggest the previously observed effect of the EDI-Cvi-0 allele on flowering time likely depends on genetic background, due to an epistatic interaction. Altogether, our results provide an empirical example of the effects demographic history and selection has on trait architecture.

ОПТИМИЗАЦИОННЫЕ МЕТОДЫ СОСТАВЛЕНИЯ РАСПИСАНИЯ НАБЛЮДЕНИЙ ЗА КОСМИЧЕСКИМИ АППАРАТАМИ В ОКОЛОЗЕМНОМ ПРОСТРАНСТВЕ НАЗЕМНЫМИ РАДИОТЕХНИЧЕСКИМИ ИЗМЕРИТЕЛЬНЫМИ СРЕДСТВАМИ

Due to a significant increase in the number of spacecrafts in low orbit, the problem of planning observations by radio instruments acquires significant importance. The paper shows that this problem can be reduced to the problem of optimization of observation time. Two metrics for plan quality evaluation are proposed (minimum value metric and geometric mean metric). It was suggested 3 optimization algorithms for planning: maximization of arithmetic mean, minimization of quadratic deviation from mean, maximization of geometric mean. A comparison of the proposed algorithms and the adaptive random walk algorithm was carried out. As a result of experimental research, it has been found out that the best quality for the chosen metrics is the maximization algorithm of geometric mean. However, the time required for calculation of the schedule is more than 65 times more than for other algorithms.

A Multi-Strategy Sparrow Search Algorithm with Selective Ensemble

Aiming at the deficiencies of the sparrow search algorithm (SSA), such as being easily disturbed by the local optimal and deficient optimization accuracy, a multi-strategy sparrow search algorithm with selective ensemble (MSESSA) is proposed. Firstly, three novel strategies in the strategy pool are proposed: variable logarithmic spiral saltation learning enhances global search capability, neighborhood-guided learning accelerates local search convergence, and adaptive Gaussian random walk coordinates exploration and exploitation. Secondly, the idea of selective ensemble is adopted to select an appropriate strategy in the current stage with the aid of the priority roulette selection method. In addition, the modified boundary processing mechanism adjusts the transgressive sparrows’ locations. The random relocation method is for discoverers and alerters to conduct global search in a large range, and the relocation method based on the optimal and suboptimal of the population is for scroungers to conduct better local search. Finally, MSESSA is tested on CEC 2017 suites. The function test, Wilcoxon test, and ablation experiment results show that MSESSA achieves better comprehensive performance than 13 other advanced algorithms. In four engineering optimization problems, the stability, effectiveness, and superiority of MSESSA are systematically verified, which has significant advantages and can reduce the design cost.

Flexible Bayesian quantile regression for nonlinear mixed effects models based on the generalized asymmetric Laplace distribution

We propose flexible Bayesian quantile regression for a class of parametric nonlinear mixed effects models for longitudinal data based on the generalized asymmetric Laplace distribution, which exhibits more flexibility in skewness, mode and tail behaviour than the frequently used asymmetric Laplace distribution in quantile regression. An efficient Markov chain Monte Carlo procedure based on the adaptive random walk Metropolis-within-Gibbs sampling algorithm is derived for posterior inference. We demonstrate through simulation studies and empirical analysis that the proposed method could provide more accurate parameter estimation and better model fit than the existing methods.

Transient mutation bias increases the predictability of evolution on an empirical genotype-phenotype landscape.

Predicting how a population will likely navigate a genotype-phenotype landscape requires consideration of selection in combination with mutation bias, which can skew the likelihood of following a particular trajectory. Strong and persistent directional selection can drive populations to ascend toward a peak. However, with a greater number of peaks and more routes to reach them, adaptation inevitably becomes less predictable. Transient mutation bias, which operates only on one mutational step, can influence landscape navigability by biasing the mutational trajectory early in the adaptive walk. This sets an evolving population upon a particular path, constraining the number of accessible routes and making certain peaks and routes more likely to be realized than others. In this work, we employ a model system to investigate whether such transient mutation bias can reliably and predictably place populations on a mutational trajectory to the strongest selective phenotype or usher populations to realize inferior phenotypic outcomes. For this we use motile mutants evolved from ancestrally non-motile variants of the microbe Pseudomonas fluorescens SBW25, of which one trajectory exhibits significant mutation bias. Using this system, we elucidate an empirical genotype-phenotype landscape, where the hill-climbing process represents increasing strength of the motility phenotype, to reveal that transient mutation bias can facilitate rapid and predictable ascension to the strongest observed phenotype in place of equivalent and inferior trajectories. This article is part of the theme issue 'Interdisciplinary approaches to predicting evolutionary biology'.

Walk for Learning: A Random Walk Approach for Federated Learning From Heterogeneous Data

We consider the problem of a Parameter Server (PS) that wishes to learn a model that fits data distributed on the nodes of a graph. We focus on Federated Learning (FL) as a canonical application. One of the main challenges of FL is the communication bottleneck between the nodes and the parameter server. A popular solution in the literature is to allow each node to do several local updates on the model in each iteration before sending it back to the PS. While this mitigates the communication bottleneck, the statistical heterogeneity of the data owned by the different nodes has proven to delay convergence and bias the model. In this work, we study random walk (RW) learning algorithms for tackling the communication and data heterogeneity problems. The main idea is to leverage available direct connections among the nodes themselves, which are typically “cheaper” than the communication to the PS. In a random walk, the model is thought of as a “baton” that is passed from a node to one of its neighbors after being updated in each iteration. The challenge in designing the RW is the data hetErogeneity and the uncertainty about the data distributions. Ideally, we would want to visit more often nodes that hold more informative data. We cast this problem as a sleeping multi-armed bandit (MAB) to design near-optimal node sampling strategy that achieves a variance reduced gradient estimates and approaches sub-linearly the optimal sampling strategy. Based on this framework, we present an adaptive random walk learning algorithm. We provide theoretical guarantees on its convergence. Our numerical results validate our theoretical findings and show that our algorithm outperforms existing random walk algorithms.

Maximal dispersion of adaptive random walks

The challenge of maximizing dispersion of a dynamical process over a globally unknown network is overcome by introducing an adaptive random walk. This adaptive random walk, through a large-deviation-theory approach, updates its transition rule on the local information collected while exploring the network.

Rate of environmental variation impacts the predictability in evolution.

In the two last decades, we have improved our understanding of the adaptive evolution of natural populations under constant and stable environments. For instance, experimental methods from evolutionary biology have allowed us to explore the structure of fitness landscapes and survey how the landscape properties can constrain the adaptation process. However, understanding how environmental changes can affect adaptation remains challenging. Very little progress has been made with respect to time-varying fitness landscapes. Using the adaptive-walk approximation, we survey the evolutionary process of populations under a scenario of environmental variation. In particular, we investigate how the rate of environmental variation influences the predictability in evolution. We observe that the rate of environmental variation not only changes the duration of adaptive walks towards fitness peaks of the fitness landscape, but also affects the degree of repeatability of both outcomes and evolutionary paths. In general, slower environmental variation increases the predictability in evolution. The accessibility of endpoints is greatly influenced by the ecological dynamics. The dependence of these quantities on the genome size and number of traits is also addressed. To our knowledge, this contribution is the first to use the predictive approach to quantify and understand the impact of the speed of environmental variation on the degree of parallelism of the evolutionary process.

Getting higher on rugged landscapes: Inversion mutations open access to fitter adaptive peaks in NK fitness landscapes.

Molecular evolution is often conceptualised as adaptive walks on rugged fitness landscapes, driven by mutations and constrained by incremental fitness selection. It is well known that epistasis shapes the ruggedness of the landscape's surface, outlining their topography (with high-fitness peaks separated by valleys of lower fitness genotypes). However, within the strong selection weak mutation (SSWM) limit, once an adaptive walk reaches a local peak, natural selection restricts passage through downstream paths and hampers any possibility of reaching higher fitness values. Here, in addition to the widely used point mutations, we introduce a minimal model of sequence inversions to simulate adaptive walks. We use the well known NK model to instantiate rugged landscapes. We show that adaptive walks can reach higher fitness values through inversion mutations, which, compared to point mutations, allows the evolutionary process to escape local fitness peaks. To elucidate the effects of this chromosomal rearrangement, we use a graph-theoretical representation of accessible mutants and show how new evolutionary paths are uncovered. The present model suggests a simple mechanistic rationale to analyse escapes from local fitness peaks in molecular evolution driven by (intragenic) structural inversions and reveals some consequences of the limits of point mutations for simulations of molecular evolution.

Strong evidence for the adaptive walk model of gene evolution in Drosophila and Arabidopsis.

Understanding the dynamics of species adaptation to their environments has long been a central focus of the study of evolution. Theories of adaptation propose that populations evolve by "walking" in a fitness landscape. This "adaptive walk" is characterised by a pattern of diminishing returns, where populations further away from their fitness optimum take larger steps than those closer to their optimal conditions. Hence, we expect young genes to evolve faster and experience mutations with stronger fitness effects than older genes because they are further away from their fitness optimum. Testing this hypothesis, however, constitutes an arduous task. Young genes are small, encode proteins with a higher degree of intrinsic disorder, are expressed at lower levels, and are involved in species-specific adaptations. Since all these factors lead to increased protein evolutionary rates, they could be masking the effect of gene age. While controlling for these factors, we used population genomic data sets of Arabidopsis and Drosophila and estimated the rate of adaptive substitutions across genes from different phylostrata. We found that a gene's evolutionary age significantly impacts the molecular rate of adaptation. Moreover, we observed that substitutions in young genes tend to have larger physicochemical effects. Our study, therefore, provides strong evidence that molecular evolution follows an adaptive walk model across a large evolutionary timescale.

Integrating the Past: A Study of Trajectory Integration and Recombinatory Depth

In this study, we aim to provide a more comprehensive account of the role of interdependence in knowledge recombination for technological invention. By integrating theory from both knowledge recombination and technological trajectory literatures, we characterize a dimension of knowledge recombination termed recombinatory depth. Following the use of NK models from evolutionary genetics, we import the concept of adaptive walks from evolutionary genetics to communicate our argument. If an inventor integrates knowledge across many sequentially-dependent antecedent technologies in the same trajectory, design improvements can be produced without negative effects on recombinatory search (much like in adaptive walks). We conceptualize this dimension as recombinatory depth and operationalize it using patent data from the European Patent Office’s PATSTAT database. An analysis of technological impact shows that high recombinatory depth has a strong positive relationship on technological impact. Moreover, we find that this first relationship is positively moderated by technological diversity, suggesting that high recombinatory depth helps to integrate distant and diverse technological trajectories. This paper is under development and further work is needed to analyze and develop our results.

Hybridization alters the shape of the genotypic fitness landscape, increasing access to novel fitness peaks during adaptive radiation.

Estimating the complex relationship between fitness and genotype or phenotype (i.e. the adaptive landscape) is one of the central goals of evolutionary biology. However, adaptive walks connecting genotypes to organismal fitness, speciation, and novel ecological niches are still poorly understood and processes for surmounting fitness valleys remain controversial. One outstanding system for addressing these connections is a recent adaptive radiation of ecologically and morphologically novel pupfishes (a generalist, molluscivore, and scale-eater) endemic to San Salvador Island, Bahamas. We leveraged whole-genome sequencing of 139 hybrids from two independent field fitness experiments to identify the genomic basis of fitness, estimate genotypic fitness networks, and measure the accessibility of adaptive walks on the fitness landscape. We identified 132 single nucleotide polymorphisms (SNPs) that were significantly associated with fitness in field enclosures. Six out of the 13 regions most strongly associated with fitness contained differentially expressed genes and fixed SNPs between trophic specialists; one gene (mettl21e) was also misexpressed in lab-reared hybrids, suggesting a potential intrinsic genetic incompatibility. We then constructed genotypic fitness networks from adaptive alleles and show that scale-eating specialists are the most isolated of the three species on these networks. Intriguingly, introgressed and de novo variants reduced fitness landscape ruggedness as compared to standing variation, increasing the accessibility of genotypic fitness paths from generalist to specialists. Our results suggest that adaptive introgression and de novo mutations alter the shape of the fitness landscape, providing key connections in adaptive walks circumventing fitness valleys and triggering the evolution of novelty during adaptive radiation.

We get by with a little help from our friends: shared adaptive variation provides a bridge to novel ecological specialists during adaptive radiation.

Adaptive radiations involve astounding bursts of phenotypic, ecological and species diversity. However, the microevolutionary processes that underlie the origins of these bursts are still poorly understood. We report the discovery of an intermediate C. sp. ‘wide-mouth’ scale-eating ecomorph in a sympatric radiation of Cyprinodon pupfishes, illuminating the transition from a widespread algae-eating generalist to a novel microendemic scale-eating specialist. We first show that this ecomorph occurs in sympatry with generalist C. variegatus and scale-eating specialist C. desquamator on San Salvador Island, Bahamas, but is genetically differentiated, morphologically distinct and often consumes scales. We then compared the timing of selective sweeps on shared and unique adaptive variants in trophic specialists to characterize their adaptive walk. Shared adaptive regions swept first in both the specialist desquamator and the intermediate ‘wide-mouth’ ecomorph, followed by unique sweeps of introgressed variation in ‘wide-mouth’ and de novo variation in desquamator. The two scale-eating populations additionally shared 9% of their hard selective sweeps with the molluscivore C. brontotheroides, despite no single common ancestor among specialists. Our work provides a new microevolutionary framework for investigating how major ecological transitions occur and illustrates how both shared and unique genetic variation can provide a bridge for multiple species to access novel ecological niches.