Symmetric M-ary phase discrimination using quantum-optical probe states

We present a theoretical study of minimum error probability discrimination, using quantum- optical probe states, of M optical phase shifts situated symmetrically on the unit circle. We assume ideal lossless conditions and full freedom for implementing quantum measurements and for probe state selection, subject only to a constraint on the average energy, i.e., photon number. In particular, the probe state is allowed to have any number of signal and ancillary modes, and to be pure or mixed. Our results are based on a simple criterion that partitions the set of pure probe states into equivalence classes with the same error probability performance. Under an energy constraint, we find the explicit form of the state that minimizes the error probability. This state is an unentangled but nonclassical single-mode state. The error performance of the optimal state is compared with several standard states in quantum optics. We also show that discrimination with zero error is possible only beyond a threshold energy of (M - 1)/2. For the M = 2 case, we show that the optimum performance is readily demonstrable with current technology. While transmission loss and detector inefficiencies lead to a nonzero erasure probability, the error rate conditional on no erasure is shown to remain the same as the optimal lossless error rate.Comment: 13 pages, 10 figure

Using error correction to determine the noise model

Quantum error correcting codes have been shown to have the ability of making quantum information resilient against noise. Here we show that we can use quantum error correcting codes as diagnostics to characterise noise. The experiment is based on a three-bit quantum error correcting code carried out on a three-qubit nuclear magnetic resonance (NMR) quantum information processor. Utilizing both engineered and natural noise, the degree of correlations present in the noise affecting a two-qubit subsystem was determined. We measured a correlation factor of c=0.5+/-0.2 using the error correction protocol, and c=0.3+/-0.2 using a standard NMR technique based on coherence pathway selection. Although the error correction method demands precise control, the results demonstrate that the required precision is achievable in the liquid-state NMR setting.Comment: 10 pages, 3 figures. Added discussion section, improved figure

Rates of convergence in active learning

We study the rates of convergence in generalization error achievable by active learning under various types of label noise. Additionally, we study the general problem of model selection for active learning with a nested hierarchy of hypothesis classes and propose an algorithm whose error rate provably converges to the best achievable error among classifiers in the hierarchy at a rate adaptive to both the complexity of the optimal classifier and the noise conditions. In particular, we state sufficient conditions for these rates to be dramatically faster than those achievable by passive learning.Comment: Published in at http://dx.doi.org/10.1214/10-AOS843 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Attention, predictive learning, and the inverse base-rate effect: Evidence from event-related potentials

We report the first electrophysiological investigation of the inverse base-rate effect (IBRE), a robust non-rational bias in predictive learning. In the IBRE, participants learn that one pair of symptoms (AB) predicts a frequently occurring disease, whilst an overlapping pair of symptoms (AC) predicts a rarely occurring disease. Participants subsequently infer that BC predicts the rare disease, a non-rational decision made in opposition to the underlying base rates of the two diseases. Error-driven attention theories of learning state that the IBRE occurs because C attracts more attention than B. On the basis of this account we predicted and observed the occurrence of brain potentials associated with visual attention: a posterior Selection Negativity, and a concurrent anterior Selection Positivity, for C vs. B in a post-training test phase. Error-driven attention theories further predict no Selection Negativity, Selection Positivity or IBRE, for control symptoms matched on frequency to B and C, but for which there was no shared symptom (A) during training. These predictions were also confirmed, and this confirmation discounts alternative explanations of the IBRE based on the relative novelty of B and C. Further, we observed higher response accuracy for B alone than for C alone; this dissociation of response accuracy (B>C) from attentional allocation (C>B) discounts the possibility that the observed attentional difference was caused by the difference in response accuracy

UPM-UC3M system for music and speech segmentation

This paper describes the UPM-UC3M system for the Albayzín evaluation 2010 on Audio Segmentation. This evaluation task consists of segmenting a broadcast news audio document into clean speech, music, speech with noise in background and speech with music in background. The UPM-UC3M system is based on Hidden Markov Models (HMMs), including a 3-state HMM for every acoustic class. The number of states and the number of Gaussian per state have been tuned for this evaluation. The main analysis during system development has been focused on feature selection. Also, two different architectures have been tested: the first one corresponds to an one-step system whereas the second one is a hierarchical system in which different features have been used for segmenting the different audio classes. For both systems, we have considered long term statistics of MFCC (Mel Frequency Ceptral Coefficients), spectral entropy and CHROMA coefficients. For the best configuration of the one-step system, we have obtained a 25.3% average error rate and 18.7% diarization error (using the NIST tool) and a 23.9% average error rate and 17.9% diarization error for the hierarchical one

Maximum principle and mutation thresholds for four-letter sequence evolution

A four-state mutation-selection model for the evolution of populations of DNA-sequences is investigated with particular interest in the phenomenon of error thresholds. The mutation model considered is the Kimura 3ST mutation scheme, fitness functions, which determine the selection process, come from the permutation-invariant class. Error thresholds can be found for various fitness functions, the phase diagrams are more interesting than for equivalent two-state models. Results for (small) finite sequence lengths are compared with those for infinite sequence length, obtained via a maximum principle that is equivalent to the principle of minimal free energy in physics.Comment: 25 pages, 16 figure

Optimization for L1-Norm Error Fitting via Data Aggregation

We propose a data aggregation-based algorithm with monotonic convergence to a global optimum for a generalized version of the L1-norm error fitting model with an assumption of the fitting function. The proposed algorithm generalizes the recent algorithm in the literature, aggregate and iterative disaggregate (AID), which selectively solves three specific L1-norm error fitting problems. With the proposed algorithm, any L1-norm error fitting model can be solved optimally if it follows the form of the L1-norm error fitting problem and if the fitting function satisfies the assumption. The proposed algorithm can also solve multi-dimensional fitting problems with arbitrary constraints on the fitting coefficients matrix. The generalized problem includes popular models such as regression and the orthogonal Procrustes problem. The results of the computational experiment show that the proposed algorithms are faster than the state-of-the-art benchmarks for L1-norm regression subset selection and L1-norm regression over a sphere. Further, the relative performance of the proposed algorithm improves as data size increases

A Pedant's Approach to Exponential Smoothing

An approach to exponential smoothing that relies on a linear single source of error state space model is outlined. A maximum likelihood method for the estimation of associated smoothing parameters is developed. Commonly used restrictions on the smoothing parameters are rationalised. Issues surrounding model identification and selection are also considered. It is argued that the proposed revised version of exponential smoothing provides a better framework for forecasting than either the Box-Jenkins or the traditional multi-disturbance state space approaches.Time Series Analysis, Prediction, Exponential Smoothing, ARIMA Models, Kalman Filter, State Space Models