### Table 4.3: The probabilities of a group of states V after 1 and after 2 times the execution of a noisy observe(2) action.

### TABLE I MSE of (1) the noisy observed image, (2) oracle soft-thresholding, (3) soft-thresholding with thresholds ~ T, and (4) quantized signal with zero-zone thresholds ~ T. The last column shows the bitrate (bits per pixel) of the quantized image. Averaged over 20 runs.

### Table 2: The actual and estimated state of a 2D robot given a series of noisy actions and observations. In this example, the covariance matrix is always diagonal with equal entries, and so for compactness we have only given one number for the variance.

### Table 1: Test functions. Signal{to{noise ratios (snrs) are de ned as snr = fvar(f)= 2g1 2 , as in Donoho and John- stone (1995). Three snr levels were used: 2, 4 and 6. For each combination of test function and snr, 50 sets of noisy observations were simulated with U[0; 1] as the design density for xi. Only one n was used: n = 200 (n and snr are interchangeable when both of them are 15

2002

"... In PAGE 18: ...Discontinuous Curves The above experiment was repeated with three discontinuous test functions. These test functions have been used by other authors, and are listed in Table1 as Test Functions 4 to 6. Observe that SK, RSW and HST are not expected to perform well, as these procedures were not designed for recovering non{smooth curves.... ..."

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### Table 4: The sensitivity of image-only batch estimation to camera intrinsics calibration errors and to image observation errors. The correct motion can be recovered from image measurements only given synthetic, zero noise observations and the intrinsics used to generate them (row 1). Estimating the motion from the synthetic image observations and a perturbed version of the camera intrinsics that generates the observations results in errors (rows 2-6) are much less than the errors that result from estimating the motion from the unperturbed camera intrinsics and noisy image observations (rows 7-11).

"... In PAGE 22: ... The estimated camera intrinsics, along with the reported standard deviations, are given in Table 3. The results are shown in rows 2-6 of Table4 . The resulting errors in the estimates are on the order of, or less, than the errors that we observe in the batch image-and-inertial estimates from the real image mea- surements.... In PAGE 22: ...0 pixels in each direction, which is the same ob- servation error distribution we have assumed in our experiments. The resulting errors are shown in rows 7-11 of Table4 , and are an order of magnitude larger... ..."

### Table 1: A typical motion computation with the synthetic noisy sequence. One can observe that the accelerations (especially _ V) are extremely noisy, whereas the kinematic screw is very accurate. This shows that the errors on the acceleration do not a ect much the accuracy of the motion and justi es a posteriori the choice of minimizing only with respect to the motion parameters (keeping the accelerations null) since this reduces dramatically the number of solutions. The dash denotes errors that are not relevant.

1995

"... In PAGE 21: ... 5.2 Results Table1 shows a typical result obtained from the synthetic sequence. It is easy to see that the obtained result are very accurate for and V and much worse for _ and specially for _ V.... ..."

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### Table 1: Setting of hyper-parameters for observation model. For the H526 data, we reduced the variance of the neutral state (bold) to 2 2 = 0:01, since the data has been median ltered and hence is less noisy than the synthetic data.

in Abstract

"... In PAGE 5: ...atrix A and the initial state distribution (i.e., we use A i = i = 1=K), since the signal can start in any state and move from any state to any other state. The remaining parameters are given weakly informative priors, as shown in Table1 and 2. These values were chosen by hand by looking at the data.... ..."

### Table 2: An example dialogue. Note that the robot chooses the correct action in the final two exchanges,even though the utterance is both noisy and ambiguous.

"... In PAGE 8: ... Note that the robot chooses the correct action in the final two exchanges,even though the utterance is both noisy and ambiguous. Table2 shows an example dialogue obtained by having an actual user interact with the system on the robot. The left-most column is the emitted observation from the speech recognition system.... ..."

### Table 5: Comparison of kernel widths derived automatically and manually from the distances histogram. Even with noisy histograms, and varying data dispersion inside clusters, where several peaks can be observed, the histogram method leads to quite acceptable results. The kernel width and the number of misclassiflcations are in most cases similar to those obtained by the best found by checking of a large range of values and using the known class labels.

2004

"... In PAGE 22: ... The pure K-means algorithm is, of course, faster. Table5 evaluates the quality of the choice of with the proposed histogram method. One can see that in most cases the chosen from the histogram is close to the best value, and the same is true even for the number of clustering errors.... ..."

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