Probability Of Large Errors Research Articles

HW/SW Co-Design for Reliable TCAM- Based In-Memory Brain-Inspired Hyperdimensional Computing

Brain-inspired hyperdimensional computing (HDC) is continuously gaining remarkable attention. It is a promising alternative to traditional machine-learning approaches due to its ability to learn from little data, lightweight implementation, and resiliency against errors. However, HDC is overwhelmingly data-centric similar to traditional machine-learning algorithms. In-memory computing is rapidly emerging to overcome the von Neumann bottleneck by eliminating data movements between compute and storage units. In this work, we investigate and model the impact of imprecise in-memory computing hardware on the inference accuracy of HDC. Our modeling is based on 14nm FinFET technology fully calibrated with Intel measurement data. We accurately model, for the first time, the voltage-dependent error probability in SRAM-based and FeFET-based in-memory computing. Thanks to HDC's resiliency against errors, the complexity of the underlying hardware can be reduced, providing large energy savings of up to 6x. Experimental results for SRAM reveal that variability-induced errors have a probability of up to 39 percent. Despite such a high error probability, the inference accuracy is only marginally impacted. This opens doors to explore new tradeoffs. We also demonstrate that the resiliency against errors is application-dependent. In addition, we investigate the robustness of HDC against errors when the underlying in-memory hardware is realized using emerging non-volatile FeFET devices instead of mature CMOS-based SRAMs. We demonstrate that inference accuracy does remain high despite the larger error probability, while large area and power savings can be obtained. All in all, HW/SW co-design is the key for efficient yet reliable in-memory hyperdimensional computing for both conventional CMOS technology and upcoming emerging technologies.

On Minimizing the Probability of Large Errors in Robust Point Cloud Registration

On Minimizing the Probability of Large Errors in Robust Point Cloud Registration

A data optimization and processing method for complex micro‐electronics system in the IoT environment

With the rapid development of network technologies nowadays, the Internet of Things (IoT) has become a comment trend in most situations. In this trend, the complex micro‐electronics system is the most benefited one. Generally, the traditional evaluation and design of the micro‐electronics system is to establish an approximate model based on the statistical theory with a large error probability. Now, with the benefits of IoT, new methods can be applied. In this paper, we mainly use the IoT enabled Back Propagation (BP) neural network to establish the reliability evaluation and analysis model of micro‐electronic complex system. Firstly, the life cycle of micro‐electronic components and mechanical parts obeys exponential distribution and Weibull distribution in the IoT environment respectively. Then the reliability of each piece under different working time and the overall reliability of the system is calculated according to the failure rate of each part. Secondly, the numerical simulation results show that the error of the reliability value between the BP reliability evaluation model and the basic reliability model is very small, which verifies the accuracy and feasibility of the model, and predicts the reliability of the system. The research shows that this method can predict the overall reliability from the reliability of components, improve the accuracy of reliability evaluation, solve the problem that it is difficult to obtain the analytical expression of distribution model based on statistical theory, and reduce the complexity of the model.

Finite sample performance of linear least squares estimation

Linear Least Squares is a well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required. Surprisingly, bounding the probability of large errors with finitely many samples has been left open, especially when dealing with correlated noise with unknown covariance. In this paper we analyze the finite sample performance of the linear least squares estimator. Using these bounds we obtain accurate bounds on the tail of the estimator’s distribution. We show the fast exponential convergence of the number of samples required to ensure a given accuracy with high probability and provide explicit formulas. We analyze a sub-Gaussian setting with a fixed or random design matrix of the linear least squares problem. We also extend the results to the case of a martingale difference noise sequence. Our analysis method is simple and uses simple L∞ type bounds on the estimation error. We demonstrate that our results are tighter than previously proposed bounds. The proposed bounds make it possible to predict the number of samples required for least squares estimation even when the least squares is sub-optimal and is used for computational simplicity.

Analysis and Reduction of Large Errors in Rayleigh-Based Distributed Sensor

Commonly, the frequency shift of back-reflection spectra is the key parameter to measure quantitatively local temperature or strain changes in frequency-scanned Rayleigh-based distributed fiber sensors. Cross correlation is the most common method to estimate the frequency shift; however, large errors may take place, particularly when the frequency shift introduced by the temperature or strain change applied to the fiber is beyond the spectral width of the main correlation peak. This fact substantially limits the reliability of the system, and therefore requires careful analysis and possible solutions. In this paper, an analytical model is proposed to thoroughly describe the probability of large errors. This model shows that the cross correlation intrinsically and inevitably leads to large errors when the sampled signal distribution is finite, even under perfect signal-to-noise ratio. As an alternative solution to overcome such a problem, least mean squares is employed to estimate the frequency shift. In addition to reducing the probability of large errors, the proposed method only requires to measure a narrow spectrum, significantly reducing the measurement time compared to state-of-the-art implementations. Both the model and the solution are experimentally verified using a frequency-scanned phase-sensitive optical time-domain reflectometry system, achieving a spatial resolution of 5 cm, with a sensing range of 860 m and an acquisition time below 15 s, over a measurable temperature range of more than 100 K with a repeatability of 20 mK, corresponding to a temperature dynamic range of 5000 resolved points.

Chemoinformatic Classification Methods and their Applicability Domain.

Classification rules are often used in chemoinformatics to predict categorical properties of drug candidates related to bioactivity from explanatory variables, which encode the respective molecular structures (i.e. molecular descriptors). To avoid predictions with an unduly large error probability, the domain the classifier is applied to should be restricted to the domain covered by the training set objects. This latter domain is commonly referred to as applicability domain in chemoinformatics. Conceptually, the applicability domain defines the region in space where the "normal" objects are located. Defining the border of the applicability domain may then be viewed as detecting anomalous or novel objects or as detecting outliers. Currently two different types of measures are in use. The first one defines the applicability domain solely in terms of the molecular descriptor space, which is referred to as novelty detection. The second type defines the applicability domain in terms of the expected reliability of the predictions which is referred to as confidence estimation. Both types are systematically differentiated here and the most popular measures are reviewed. It will be shown that all common chemoinformatic classifiers have built-in confidence scores. Since confidence estimation uses information of the class labels for computing the confidence scores, it is expected to be more efficient in reducing the error rate than novelty detection, which solely uses the information of the explanatory variables.

Entanglement generation by communication using squeezed states

In order to improve the error probability of generating entanglement by communication for quantum computation, we propose the use of squeezed light. When generating entanglement between two atoms by communication, the error probability can be reduced by increasing the distance between quantum states of probe light in phase space. The phase rotation of light depends on the atom-photon coupling strength and the light amplitude, which are limited in practice. A large error probability has been expected for coherent probe light. If we assume typical values of light amplitude and phase rotation, $\ensuremath{\alpha}=100$ and $\ensuremath{\theta}=0.01$, the error probability is estimated to be ${P}_{\mathrm{coh}}^{(\mathrm{min})}=0.14$ and ${P}_{\mathrm{coh}}^{(\mathrm{hom})}=0.23$ for minimum error discrimination and homodyne measurements. The error probability can be reduced to ${P}_{\mathrm{squ}}^{(\mathrm{min})}=1.73\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ and ${P}_{\mathrm{squ}}^{(\mathrm{hom})}=4.09\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ using squeezed coherent light, where the same values of the mean photon number and the phase rotation angle are assumed for the coherent light probe. These values satisfy the requirements for scalable quantum computation.

On Transmission of Multiresolution Gaussian Sources over Noisy Relay Networks

This paper investigates joint source-channel coding (JSCC) in a decode-and-forward three-node relay network, in which scalable source coding (SSC) is coupled with superposition coding (SPC) to form a layered coding architecture of SSC-SPC. In contrast to any previously reported research using asymptotic capacity-based distortion (CBD) measure, we derive the mean-squared error end-to-end distortion (EED) of such JSCC system based on a real-valued Gaussian source, aiming to achieve better precision and practicality for applications in which channels are subject to large error probabilities. The EED evaluation is formulated and applied to demonstrate achievable gains of the SSC-SPC architecture versus a number of conventional approaches. Power allocation optimization is performed based on the developed non-asymptotic EED model and compared to that by using an asymptotic CBD measure in which symbol losses caused by channel error cannot be considered. We demonstrate the performance gaps between results solved from EED versus CBD in our numerical example, and conclude that the optimization using CBD behaves awkwardly in computing proper power allocation configurations in the considered SSC-SPC architecture.

Distribution-Invariant Risk Measures, Entropy, and Large Deviations

The simulation of distributions of financial assets is an important issue for financial institutions. If risk measures are evaluated for a simulated distribution instead of the model-implied distribution, the errors in the risk measurements need to be analyzed. For distribution-invariant risk measures which are continuous on compacts, we employ the theory of large deviations to study the probability of large errors. If the approximate risk measurements are based on the empirical distribution of independent samples, then the rate function equals the minimal relative entropy under a risk measure constraint. We solve this minimization problem explicitly for shortfall risk and average value at risk.

Distribution-Invariant Risk Measures, Entropy, and Large Deviations

The simulation of distributions of financial assets is an important issue for financial institutions. If risk measures are evaluated for a simulated distribution instead of the model-implied distribution, the errors in the risk measurements need to be analyzed. For distribution-invariant risk measures which are continuous on compacts, we employ the theory of large deviations to study the probability of large errors. If the approximate risk measurements are based on the empirical distribution of independent samples, then the rate function equals the minimal relative entropy under a risk measure constraint. We solve this minimization problem explicitly for shortfall risk and average value at risk.

Nonrandom quantization errors in timebases

Timebase distortion causes nonlinear distortion of waveforms measured by sampling instruments. When such instruments are used to measure the RMS amplitude of the sampled waveforms, such distortions result in errors in the measured RMS values. This paper looks at the nature of the errors that result from nonrandom quantization errors in an instrument timebase circuit. Simulations and measurements on a sampling voltmeter show that the errors in measured RMS amplitude have a nonnormal probability distribution, such that the probability of large errors is much greater than would be expected from the usual quantization noise model. A novel timebase compensation method is proposed which makes the measured RMS errors normally distributed and reduces their standard deviation by a factor of 25. This compensation method was applied to a sampling voltmeter and the improved accuracy was realized.

Weiss–Weinstein bound for matched-field parameter estimation

Matched-field parameter estimation, including source localization and environmental parameter estimation, is often implemented based on an ambiguity surface. The ambiguity surface is derived from the correlation between the observed signal field and the modeled signal field, and is often characterized by a multimodal structure since the typical signal field is a highly nonlinear function of the embedded parameters. In the presence of noise or other interferences, a high sidelobe level leads to a large error probability in parameter estimation. This sidelobe effect increases as the signal-to-noise ratio (SNR) decreases such that, below a threshold SNR, the estimation mean-square-error (MSE) is dominated by the error around the sidelobes, which is not predicted by the Cramer-Rao bound (CRB). To analyze this effect, the Weiss–Weinstein bound (WWB) is presented for the attainable performance of matched field methods. The bound is expressed in terms of the SNR and an ambiguity function defined based on the Green’s function both at the receiver array. An evaluation example demonstrates how the ambiguity behavior, particularly the sidelobe structure, affects the bound’s evaluation in different SNR regions and leads to the well-known threshold phenomenon in nonlinear parameter estimation.

Repeated convolutional codes for high-error-rate channels

An error-correction scheme for an M-ary symmetric channel (MSC) characterized by a large error probability p/sub e/ is considered. The value of p/sub e/ can be near, but smaller than, 1-1/M, for which the channel capacity is zero, such as may occur in a jamming environment. The coding scheme consists of an outer convolutional code and an inner repetition code of length m that is used for each convolutional code symbol. At the receiving end, the m inner code symbols are used to form a soft-decision metric, which is passed to a soft-decision decoder for the convolutional code. The effect of finite quantization and methods to generate binary metrics for M>2 are investigated. Monte Carlo simulation results are presented. For the binary symmetric channel (BSC), it is shown that the overall code rate is larger than 0.6R/sub 0/, where R/sub 0/ is the cutoff rate of the channel. New union bounds on the bit error probability for systems with a binary convolutional code on 4-ary and 8-ary orthogonal channels are presented. For a BSC and a large m, a method is presented for BER approximation based on the central limit theorem.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Analysis methods for optical heterodyne DPSK receivers corrupted by laser phase noise

Two methods are presented for analyzing the effects of phase noise on the performance of an optical heterodyne binary differential-(DPSK) system. The first method utilizes a perturbation solution for filtered phase noise. By comparing the results of this analysis with simulated results, it is shown that the perturbation solution is accurate for laser linewidths up to at least 10% of the bit rate. Using this analysis, the accuracy of the widely used approximation, whereby the effects of filtering on the magnitude of the phase-noise corrupted signal are neglected, is verified. The author's second method is based on moments of random variables. As the level of phase noise in a practical DPSK system must be small, an improved formulation for the moments of the filtered phase noise is derived. It removes the major cause of this numerical instability. A maximum-entropy probability density function estimation technique is applied to the problem of analyzing the performance of a DPSK receiver. By comparing results with those obtained using the perturbation analysis, it is found that the moment-based method is effectively limited to relatively large error probabilities.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Basic properties and prediction of max-ARMA processes

A max-autoregressive moving average (MARMA(p, q)) process {Xt } satisfies the recursion for all t where φ i , , and {Zt } is i.i.d. with common distribution function Φ1,σ (X): = exp {–σ x –1} for . Such processes have finite-dimensional distributions which are max-stable and hence are examples of max-stable processes. We provide necessary and sufficient conditions for existence of a stationary solution to the MARMA recursion and we examine the reducibility of the process to a MARMA(p′, q′) with p′ &amp;lt;p or q′ &amp;lt; q . After introducing a natural metric between two jointly max-stable random variables, we consider the prediction problem for MARMA processes. Assuming that X 1, …, Xn have been observed, we restrict our class of predictors to be max-linear, i.e. of the form , and find b 1, …, bn to minimize the distance between this predictor and Xn+k for k 1. The optimality criterion is designed to minimize the probability of large errors and is similar in spirit to the dispersion criterion adopted in Cline and Brockwell (Stoch. Proc. Appl. 19 (1985), 281-296) for the prediction of ARMA processes with stable noise. Most of our results remain valid for the case when the distribution of Z 1 is only in the domain of attraction of Φ1,σ . In addition, we give a naive estimation procedure for the φ 's and the θ 's which, with probability 1, identifies the true parameter values exactly for n sufficiently large.

Basic properties and prediction of max-ARMA processes

A max-autoregressive moving average (MARMA(p, q)) process {Xt} satisfies the recursion for all t where φ i, , and {Zt} is i.i.d. with common distribution function Φ1,σ (X): = exp {–σ x–1} for . Such processes have finite-dimensional distributions which are max-stable and hence are examples of max-stable processes. We provide necessary and sufficient conditions for existence of a stationary solution to the MARMA recursion and we examine the reducibility of the process to a MARMA(p′, q′) with p′ &lt;p or q′ &lt; q. After introducing a natural metric between two jointly max-stable random variables, we consider the prediction problem for MARMA processes. Assuming that X1, …, Xn have been observed, we restrict our class of predictors to be max-linear, i.e. of the form , and find b1, …, bn to minimize the distance between this predictor and Xn+k for k 1. The optimality criterion is designed to minimize the probability of large errors and is similar in spirit to the dispersion criterion adopted in Cline and Brockwell (Stoch. Proc. Appl. 19 (1985), 281-296) for the prediction of ARMA processes with stable noise. Most of our results remain valid for the case when the distribution of Z1 is only in the domain of attraction of Φ1,σ. In addition, we give a naive estimation procedure for the φ 's and the θ 's which, with probability 1, identifies the true parameter values exactly for n sufficiently large.

Poisson models and mean-squared error for correlator estimator of time delay

A method for modeling large errors in correlation-based time-delay estimation is developed in terms of level-crossing probabilities. The level-crossing interpretation for peak ambiguity leads directly to an exact expression for the probability of large error involving the hazard function associated with the level-crossing process. Two models for the distribution of the error over the level-crossing time yield approximations to the mean-square error (MSE) that involve the low-order ( >

Measures for the optimum estimation of audiometric thresholds from the auditory brainstem response potentials.

Auditory brainstem response potentials were recorded from normally hearing subjects using a wide range of stimulus intensities including a below-threshold condition. Various measures, including the traditional Jewett V (JV) amplitude, were taken from the recordings. The probability of incorrectly concluding that a response was present was found by analysing the distribution of the JV amplitude in the no-stimulus recordings and setting an amplitude of 100 nV as the criterion of whether or not a response is deemed to be present. This probability was used to define equivalent criteria for the other measures and evoked potential (EP) thresholds could then be found for each subject and stimulus by finding the lowest stimulus intensity at which the value of the measure being considered was at or above this criterion value. Two measures were found to give significantly lower and less variable EP thresholds than the others; JV amplitude taking into account the JV latency and a self-template measure involving the correlation between the response waveforms at a high stimulus intensity level and the test intensity level. The latter measure indicates that a template-matching method of threshold estimation might be as reliable for this purpose as the measurement of JV amplitude and has the potential diagnostic advantage over JV measurements that it could be readily used with a fully objective automatic threshold evaluation protocol. The probability of making a false-positive error was found to be disconcertingly high at 0.5 for single measures and 0.22 for complex measures. This underlines the need for replicates to be taken as this dramatically reduces the probability of large errors in threshold estimation.

Large and small error performance limits for multipath time delay estimation

The Cramer-Rao lower bound (CRLB) and a lower bound on the probability of large errors for multipath time delay estimation, for a single resolvable multipath, are developed. These theoretical results are compared to the performance of the maximum likelihood estimator (MLE) and an autocorrelator, via computer simulation. For small errors and large SNR, the MLE reaches the CRLB; the variance of the time delay estimate for the autocorrelator is much larger than the CRLB if the reflection coefficient for the delayed path is near unity. For small errors and small SNR, the MLE reduces to an autocorrelator, hence, their performance is identical. For large errors and bandwidth time products greater than 500, the error probability for the autocorrelator is within 1 dB in input SNR of the lower bound on large error probability. Thus, the autocorrelator is nearly an optimal instrumentation from the point of view of large errors, at least for large bandwidth time products and the flat, low-pass spectrum considered here.

Lower bounds on worst case probability of large error for two channel time delay estimation

A lower bound on the worst case probability of large error for two channel time delay estimation using random signals is developed. The bound is based on the minimum probability of error M-ary hypothesis test using a maximum likelihood estimator (MLE). The bound can only be evaluated approximately; however, it can be determined arbitrarily well via simulation if the MLE can be instrumented. The bound is evaluated in detail for uniform, lowpass signal and noise spectra and large bandwidth time product. It is then compared with another lower bound based on a binary hypothesis test, with computer simulation results for an approximate MLE instrumentation, and with an upper bound established via computer simulation for a correlator. For a uniform, lowpass spectrum the M-ary bound is shown to be very nearly a greatest lower bound over the full range of input signal to noise ratio. Further, the correlator is shown to be very nearly an optimal instrumentation in the sense of reaching the minimum probability of large error.