We study the problem of controlling a partially observed Markov decision process (POMDP) to either aid or hinder the estimation of its state trajectory. We encode the estimation objectives via the smoother entropy, which is the conditional entropy of the state trajectory given measurements and controls. Consideration of the smoother entropy contrasts with previous approaches that instead resort to marginal (or instantaneous) state entropies due to tractability concerns. By establishing novel expressions for the smoother entropy in terms of the POMDP belief state, we show that both the problems of minimising and maximising the smoother entropy in POMDPs can surprisingly be reformulated as belief-state Markov decision processes with concave cost and value functions. The significance of these reformulations is that they render the smoother entropy a tractable optimisation objective, with structural properties amenable to the use of standard POMDP solution techniques for both active estimation and obfuscation. Simulations illustrate that optimisation of the smoother entropy leads to superior trajectory estimation and obfuscation compared to alternative approaches.
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Robots have become ubiquitous tools in various industries and households, highlighting the importance of human-robot interaction (HRI). This has increased the need for easy and accessible communication between humans and robots. Recent research has focused on the intersection of virtual assistant technology, such as Amazon's Alexa, with robots and its effect on HRI. This paper presents the Virtual Assistant, Human, and Robots in the loop (VAHR) system, which utilizes bidirectional communication to control multiple robots through Alexa. VAHR's performance was evaluated through a human-subjects experiment, comparing objective and subjective metrics of traditional keyboard and mouse interfaces to VAHR. The results showed that VAHR required 41% less Robot Attention Demand and ensured 91% more Fan-out time compared to the standard method. Additionally, VAHR led to a 62.5% improvement in multi-tasking, highlighting the potential for efficient human-robot interaction in physically- and mentally-demanding scenarios. However, subjective metrics revealed a need for human operators to build confidence and trust with this new method of operation.
Without writing a single line of code by a human, an example Monte Carlo simulation based application for stochastic dependence modeling with copulas is developed using a state-of-the-art large language model (LLM) fine-tuned for conversations. This includes interaction with ChatGPT in natural language and using mathematical formalism, which, under careful supervision by a human-expert, led to producing a working code in MATLAB, Python and R for sampling from a given copula model, evaluation of the model's density, performing maximum likelihood estimation, optimizing the code for parallel computing for CPUs as well as for GPUs, and visualization of the computed results. In contrast to other emerging studies that assess the accuracy of LLMs like ChatGPT on tasks from a selected area, this work rather investigates ways how to achieve a successful solution of a standard statistical task in a collaboration of a human-expert and artificial intelligence (AI). Particularly, through careful prompt engineering, we separate successful solutions generated by ChatGPT from unsuccessful ones, resulting in a comprehensive list of related pros and cons. It is demonstrated that if the typical pitfalls are avoided, we can substantially benefit from collaborating with an AI partner. For example, we show that if ChatGPT is not able to provide a correct solution due to a lack of or incorrect knowledge, the human-expert can feed it with the correct knowledge, e.g., in the form of mathematical theorems and formulas, and make it to apply the gained knowledge in order to provide a solution that is correct. Such ability presents an attractive opportunity to achieve a programmed solution even for users with rather limited knowledge of programming techniques.
Entropy measures are effective features for time series classification problems. Traditional entropy measures, such as Shannon entropy, use probability distribution function. However, for the effective separation of time series, new entropy estimation methods are required to characterize the chaotic dynamic of the system. Our concept of Neural Network Entropy (NNetEn) is based on the classification of special datasets (MNIST-10 and SARS-CoV-2-RBV1) in relation to the entropy of the time series recorded in the reservoir of the LogNNet neural network. NNetEn estimates the chaotic dynamics of time series in an original way. Based on the NNetEn algorithm, we propose two new classification metrics: R2 Efficiency and Pearson Efficiency. The efficiency of NNetEn is verified on separation of two chaotic time series of sine mapping using dispersion analysis (ANOVA). For two close dynamic time series (r = 1.1918 and r = 1.2243), the F-ratio has reached the value of 124 and reflects high efficiency of the introduced method in classification problems. The EEG signal classification for healthy persons and patients with Alzheimer disease illustrates the practical application of the NNetEn features. Our computations demonstrate the synergistic effect of increasing classification accuracy when applying traditional entropy measures and the NNetEn concept conjointly. An implementation of the algorithms in Python is presented.
Delay alignment modulation (DAM) is a promising technology for inter-symbol interference (ISI)-free communication without relying on sophisticated channel equalization or multi-carrier transmissions. The key ideas of DAM are delay precompensation and path-based beamforming, so that the multi-path signal components will arrive at the receiver simultaneously and constructively, rather than causing the detrimental ISI. However, the practical implementation of DAM requires channel state information (CSI) at the transmitter side. Therefore, in this letter, we study an efficient channel estimation method for DAM based on block orthogonal matching pursuit (BOMP) algorithm, by exploiting the block sparsity of the channel vector. Based on the imperfectly estimated CSI, the delay pre-compensations and tap-based beamforming are designed for DAM, and the resulting performance is studied. Simulation results demonstrate that with the BOMP-based channel estimation method, the CSI can be effectively acquired with low training overhead, and the performance of DAM based on estimated CSI is comparable to the ideal case with perfect CSI.
Data-driven offline model-based optimization (MBO) is an established practical approach to black-box computational design problems for which the true objective function is unknown and expensive to query. However, the standard approach which optimizes designs against a learned proxy model of the ground truth objective can suffer from distributional shift. Specifically, in high-dimensional design spaces where valid designs lie on a narrow manifold, the standard approach is susceptible to producing out-of-distribution, invalid designs that "fool" the learned proxy model into outputting a high value. Using an ensemble rather than a single model as the learned proxy can help mitigate distribution shift, but naive formulations for combining gradient information from the ensemble, such as minimum or mean gradient, are still suboptimal and often hampered by non-convergent behavior. In this work, we explore alternate approaches for combining gradient information from the ensemble that are robust to distribution shift without compromising optimality of the produced designs. More specifically, we explore two functions, formulated as convex optimization problems, for combining gradient information: multiple gradient descent algorithm (MGDA) and conflict-averse gradient descent (CAGrad). We evaluate these algorithms on a diverse set of five computational design tasks. We compare performance of ensemble MBO with MGDA and ensemble MBO with CAGrad with three naive baseline algorithms: (a) standard single-model MBO, (b) ensemble MBO with mean gradient, and (c) ensemble MBO with minimum gradient. Our results suggest that MGDA and CAGrad strike a desirable balance between conservatism and optimality and can help robustify data-driven offline MBO without compromising optimality of designs.
Inspired by the swarming or flocking of animal systems we study groups of agents moving in unbounded 2D space. Individual trajectories derive from a ``bottom-up'' principle: individuals reorient to maximise their future path entropy over environmental states. This can be seen as a proxy for keeping options open, a principle that may confer evolutionary fitness in an uncertain world. We find an ordered (co-aligned) state naturally emerges, as well as disordered states or rotating clusters; similar phenotypes are observed in birds, insects and fish, respectively. The ordered state exhibits an order-disorder transition under two forms of noise: (i) standard additive orientational noise, applied to the post-decision orientations (ii) ``cognitive'' noise, overlaid onto each individual's model of the future paths of other agents. Unusually, the order increases at low noise, before later decreasing through the order-disorder transition as the noise increases further.
To simulate bosons on a qubit- or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search for practical quantum applications, it is important to know how big the truncation errors can be. In general, it is not easy to estimate errors unless we have a good quantum computer. In this paper we show that traditional sampling methods on classical devices, specifically Markov Chain Monte Carlo, can address this issue with a reasonable amount of computational resources available today. As a demonstration, we apply this idea to the scalar field theory on a two-dimensional lattice, with a size that goes beyond what is achievable using exact diagonalization methods. This method can be used to estimate the resources needed for realistic quantum simulations of bosonic theories, and also, to check the validity of the results of the corresponding quantum simulations.
Completely random measures (CRMs) provide a broad class of priors, arguably, the most popular, for Bayesian nonparametric (BNP) analysis of trait allocations. As a peculiar property, CRM priors lead to predictive distributions that share the following common structure: for fixed prior's parameters, a new data point exhibits a Poisson (random) number of ``new'' traits, i.e., not appearing in the sample, which depends on the sampling information only through the sample size. While the Poisson posterior distribution is appealing for analytical tractability and ease of interpretation, its independence from the sampling information is a critical drawback, as it makes the posterior distribution of ``new'' traits completely determined by the estimation of the unknown prior's parameters. In this paper, we introduce the class of transform-scaled process (T-SP) priors as a tool to enrich the posterior distribution of ``new'' traits arising from CRM priors, while maintaining the same analytical tractability and ease of interpretation. In particular, we present a framework for posterior analysis of trait allocations under T-SP priors, showing that Stable T-SP priors, i.e., T-SP priors built from Stable CRMs, lead to predictive distributions such that, for fixed prior's parameters, a new data point displays a negative-Binomial (random) number of ``new'' traits, which depends on the sampling information through the number of distinct traits and the sample size. Then, by relying on a hierarchical version of T-SP priors, we extend our analysis to the more general setting of trait allocations with multiple groups of data or subpopulations. The empirical effectiveness of our methods is demonstrated through numerical experiments and applications to real data.
Satellite-based Synthetic Aperture Radar (SAR) images can be used as a source of remote sensed imagery regardless of cloud cover and day-night cycle. However, the speckle noise and varying image acquisition conditions pose a challenge for change detection classifiers. This paper proposes a new method of improving SAR image processing to produce higher quality difference images for the classification algorithms. The method is built on a neural network-based mapping transformation function that produces artificial SAR images from a location in the requested acquisition conditions. The inputs for the model are: previous SAR images from the location, imaging angle information from the SAR images, digital elevation model, and weather conditions. The method was tested with data from a location in North-East Finland by using Sentinel-1 SAR images from European Space Agency, weather data from Finnish Meteorological Institute, and a digital elevation model from National Land Survey of Finland. In order to verify the method, changes to the SAR images were simulated, and the performance of the proposed method was measured using experimentation where it gave substantial improvements to performance when compared to a more conventional method of creating difference images.
The growing energy and performance costs of deep learning have driven the community to reduce the size of neural networks by selectively pruning components. Similarly to their biological counterparts, sparse networks generalize just as well, if not better than, the original dense networks. Sparsity can reduce the memory footprint of regular networks to fit mobile devices, as well as shorten training time for ever growing networks. In this paper, we survey prior work on sparsity in deep learning and provide an extensive tutorial of sparsification for both inference and training. We describe approaches to remove and add elements of neural networks, different training strategies to achieve model sparsity, and mechanisms to exploit sparsity in practice. Our work distills ideas from more than 300 research papers and provides guidance to practitioners who wish to utilize sparsity today, as well as to researchers whose goal is to push the frontier forward. We include the necessary background on mathematical methods in sparsification, describe phenomena such as early structure adaptation, the intricate relations between sparsity and the training process, and show techniques for achieving acceleration on real hardware. We also define a metric of pruned parameter efficiency that could serve as a baseline for comparison of different sparse networks. We close by speculating on how sparsity can improve future workloads and outline major open problems in the field.
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