Fano’s inequality is one of the most elementary, ubiquitous, and important tools in information theory. Using majorization theory, Fano’s inequality is generalized to a broad class of information ...measures, which contains those of Shannon and Rényi. When specialized to these measures, it recovers and generalizes the classical inequalities. Key to the derivation is the construction of an appropriate conditional distribution inducing a desired marginal distribution on a countably infinite alphabet. The construction is based on the infinite-dimensional version of Birkhoff’s theorem proven by Révész Acta Math. Hungar. 1962, 3, 188–198, and the constraint of maintaining a desired marginal distribution is similar to coupling in probability theory. Using our Fano-type inequalities for Shannon’s and Rényi’s information measures, we also investigate the asymptotic behavior of the sequence of Shannon’s and Rényi’s equivocations when the error probabilities vanish. This asymptotic behavior provides a novel characterization of the asymptotic equipartition property (AEP) via Fano’s inequality.
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In this study, we consider the data compression with side information available at both the encoder and the decoder. The information source is assigned to a variable-length code that does not have to ...satisfy the prefix-free constraints. We define several classes of codes whose codeword lengths and error probabilities satisfy worse-case criteria in terms of side-information. As a main result, we investigate the exact first-order asymptotics with second-order bounds scaled as Θ(√n) as blocklength n increases under the regime of nonvanishing error probabilities. To get this result, we also derive its one-shot bounds by employing the cutoff operation.
This study considers the unconditional smooth Rényi entropy proposed by Renner and Wolf ASIACRYPT, 2005, the smooth conditional Rényi entropy proposed by Kuzuoka IEEE Trans. Inf. Th., 66(3), ...1674-1690, 2020, and a novel quantity which we term the conditional smooth -⋆ entropy. The latter two quantities can be specialized to the first in the absence of side-information. We explore the operational roles of these smooth Rényi entropies by establishing one-shot coding theorems for several information-theoretic problems, including Campbell's source coding problem, the Arıkan-Massey guessing problem, and the Bunte-Lapidoth task encoding problem. We consider these problems in cases where the errors are non-vanishing and for each problem, we consider two error formalisms: the average and maximum error criteria, where the averaging and maximization are taken with respect to the side-information. Using the one-shot coding theorems, we conclude that Kuzuoka's smooth conditional Rényi entropy and the conditional smooth-⋆ entropy are the solutions to the problems involving the average and maximum error criteria, respectively. Furthermore, we examine asymptotic expansions of these entropies when the underlying source with its side-information is stationary and memoryless. Applying our asymptotic expansions to the one-shot coding theorems, we derive various fundamental limits for these problems. We show that, under non-degenerate settings, the first-order fundamental limits differ under the average and maximum error criteria. This is in contrast to a different but related setting considered by the present authors IEEE Trans. Inf. Th., 66(12), 7565-7587, 2020, for variable-length conditional source coding allowing errors, in which the first-order terms are identical but the second-order terms are different under these error criteria.
Variable-length compression without prefix-free constraints and with side-information available at both encoder and decoder is considered. Instead of requiring the code to be error-free, we allow for ...it to have a non-vanishing error probability. We derive one-shot bounds on the optimal average codeword length by proposing two new information quantities; namely, the conditional and unconditional <inline-formula> <tex-math notation="LaTeX">\varepsilon </tex-math></inline-formula>-cutoff entropies. Using these one-shot bounds, we obtain the second-order asymptotics of the problem under two different formalisms-the average and maximum probabilities of error over the realization of the side-information. While the first-order terms in the asymptotic expansions for both formalisms are identical, we find that the source dispersion under the average error formalism is, in most cases, strictly smaller than its maximum error counterpart. Applications to a certain class of guessing problems, previously studied by Kuzuoka (2020), are also discussed.
This paper examines the exact ranges between the symmetric capacity and Gallager's reliability function E 0 for ternary-input discrete memoryless channels (T-DMCs) under a uniform input distribution. ...We first derive the two extremal ternary-input strongly symmetric channels taking the maximum and minimum values of the E 0 function among all ternary-input strongly symmetric channels with a fixed capacity. Extending the results of ternary-input strongly symmetric channels, we second derive the exact ranges between capacity and the E 0 function for ternary-input Gallager-symmetric channels. We third show that the exact ranges between the symmetric capacity and the E 0 function of T-DMCs coincide with the ranges of ternaryinput Gallager-symmetric channels. In particular, we identify the extremal channels taking the maximum and minimum of E 0 among all T-DMCs with a fixed symmetric capacity. As applications of the results, we describe some bounds of error exponents for T-DMCs with a fixed symmetric capacity.
This study investigates the fundamental limits of variable-length compression in which prefix-free constraints are not imposed (i.e., one-to-one codes are studied) and non-vanishing error ...probabilities are permitted. Due in part to a crucial relation between the variable-length and fixed-length compression problems, our analysis requires a careful and refined analysis of the fundamental limits of fixed-length compression in the setting where the error probabilities are allowed to approach either zero or one polynomially in the blocklength. To obtain the refinements, we employ tools from moderate deviations and strong large deviations. Finally, we provide the third-order asymptotics for the problem of variable-length compression with non-vanishing error probabilities. We show that unlike several other information-theoretic problems in which the third-order asymptotics are known, for the problem of interest here, the third-order term depends on the permissible error probability.
AbstractTo correctly evaluate the effects of treatments, conducting randomized controlled trials (RCTs) is a reasonable approach. However, because it is generally difficult to implement RCTs for all ...treatments, methods to estimate the treatment effects using observational data have been actively studied and used in various decision-making processes. Observational data accumulated in business activities and elsewhere contains the results of various previously implemented treatments, and correctly estimating the effects of any given treatment without separating the impacts of other treatments is challenging. Against this background, this paper proposes a method to estimate the effects of multiple treatments of various types while considering various causal relationships. Specifically, the proposal is a variational inference method that estimates the effect of multiple treatments using four latent factors estimated from observations, making assumptions that are independent of the type and number of treatments. The proposed method makes it possible to appropriately estimate the effects of measures even in situations with complex causal relationships. In addition, in situations where measures with continuous parameters are being implemented, it is possible to estimate the effects of measures that have not been implemented in the past by treating the content of the measures as a continuous variable.
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The spatial distribution of the two‐spotted spider mite Tetranychus urticae Koch is biased toward the lower surfaces of leaves as compared with the upper leaf surfaces on their host plants. Because ...of the deleterious effects of solar ultraviolet (UV) irradiation, we hypothesized T. urticae remains on lower leaf surfaces as an adaptation to avoid solar UV radiation (UVR). We examined the effects of solar UVR components on females and tested whether spatial distribution was associated with solar UVR avoidance. Attenuation of solar UVR using UV opaque film increased fecundity and reduced the movement of females from the upper to the lower leaf surfaces. In contrast, diverting solar UVR to the lower leaf surface using a light reflection sheet caused the mites to move from the lower to the upper leaf surfaces; however, attenuated UV reflection did not, suggesting that they occupy the lower leaf surface to avoid solar UVR. In monochromatic UVR tests, no eggs hatched when placed under 280–300 nm radiation, whereas almost all eggs hatched at 320–360 nm. Adult females, however, did not avoid wavelengths of 280 and 300 nm, but avoided 320–340 nm. We conclude that T. urticae exploit UVA information to avoid ambient UVB radiation.
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In recent years, marketing has often relied on using attribute information associated with the accounts registered in online services. However, most people use such services without a personal ...account, and it is impossible to obtain attribute information for these unregistered users. To deal with this situation, semi-supervised learning is an effective way to increase the number of users with attribute information. Attributes can be predicted from the historical data of unregistered users, having the historical data of registered users who have attribute information. One such semi-supervised learning method is the ladder network, which is a neural-network-based model that adds and removes noise. This model provided highly accurate predictions for image data and is also considered to be useful for predicting user attributes from historical data, where the feature vector is high-dimensional. However, this method does not account for cases where the label takes an ordered value, such as the user’s age category. In this study, we propose an extended model based on a ladder network that incorporates a mechanism that can appropriately predict a user’s attribute information, including ordinal-scale variables. We also conducted an evaluation experiment using browsing history data to demonstrate the effectiveness of the proposed method.
The development of hematopoietic stem cell (HSCs) gene therapy for DNA repair disorders, such as Fanconi anemia and Bloom syndrome, is challenging because of the induction of HSCs apoptosis by ...cytokine stimulation. Although the Baboon envelope pseudotyped lentiviral vector (BaEV-Rless-LV) has been reported as a non-stimulatory gene transfer tool, the virus titer of BaEV-Rless-LV is too low for use in clinical applications. Transfected 293 T cells with helper plasmids, including the BaEV-Rless plasmid, showed morphological changes, such as syncytium formation and detachment. To establish a novel protocol for producing a high titer of BaEV-Rless-LV, we optimized three aspects of a basic virus production protocol by focusing on modifying culture conditions and the use of reagents: the virus titer increased 3-fold when the amount of BaEV-Rless plasmid was increased 1.2-fold; the highest titer was obtained when the viral supernatant was harvested at 48-h post-transfection, despite complete syncytium formation and detachment of the 293 T cells; and the use of poly-L-lysine-coated culture plates to enhance the adhesion and proliferation of 293 T cells and prevent detachment doubled the titer. Collectively, our novel protocol resulted in a 10-fold titer increase compared to the basic protocol and may be useful in clinical applications for treating DNA repair disorders.
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•Hematopoietic stem cell gene therapy for DNA repair disorders is challenging.•BaEV-Rless pseudotyped lentiviral vector could solve the issue by cytokine depletion.•Although the titer is too low, novel virus production protocol is needed.•We modified protocol focusing on syncytium and detachment of transfected 293 T cells.•Our novel protocol resulted in a 10-fold titer increase compared to basic protocol.
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