This work considers the problem of depth completion, with or without image data, where an algorithm may measure the depth of a prescribed limited number of pixels. The algorithmic challenge is to choose pixel positions strategically and dynamically to maximally reduce overall depth estimation error. This setting is realized in daytime or nighttime depth completion for autonomous vehicles with a programmable LiDAR. Our method uses an ensemble of predictors to define a sampling probability over pixels. This probability is proportional to the variance of the predictions of ensemble members, thus highlighting pixels that are difficult to predict. By additionally proceeding in several prediction phases, we effectively reduce redundant sampling of similar pixels. Our ensemble-based method may be implemented using any depth-completion learning algorithm, such as a state-of-the-art neural network, treated as a black box. In particular, we also present a simple and effective Random Forest-based algorithm, and similarly use its internal ensemble in our design. We conduct experiments on the KITTI dataset, using the neural network algorithm of Ma et al. and our Random Forest-based learner for implementing our method. The accuracy of both implementations exceeds the state of the art. Compared with a random or grid sampling pattern, our method allows a reduction by a factor of 4-10 in the number of measurements required to attain the same accuracy.

This work examines online linear optimization with full information and switching costs (SCs) and focuses on regret bounds that depend on properties of the loss sequences. The SCs considered are bounded functions of a pair of decisions, and regret is augmented with the total SC. We show under general conditions that for any normed SC, σ(\mathbfx,\mathbfx’)=\|\mathbfx-\mathbfx’\|, regret \textitcannot be bounded given only a bound Q on the quadratic variation of losses. With an additional bound Λon the total length of losses, we prove O(\sqrtQ+Λ) regret for Regularized Follow the Leader (RFTL). Furthermore, an O(\sqrtQ) bound holds for RFTL given a cost \|\mathbfx-\mathbfx’\|^2. By generalizing the Shrinking Dartboard algorithm, we also show an expected regret bound for the best expert setting with any SC, given bounds on the total loss of the best expert and the quadratic variation of any expert. As SCs vanish, all our bounds depend purely on quadratic variation. We apply our results to pricing options in an arbitrage-free market with proportional transaction costs. In particular, we upper bound the price of “at the money” call options, assuming bounds on the quadratic variation of a stock price and the minimum of summed gains and summed losses.

We study regret minimization bounds in which the dependence on the number of experts is replaced by measures of the realized complexity of the expert class. The measures we consider are defined in retrospect given the realized losses. We concentrate on two interesting cases. In the first, our measure of complexity is the number of different “leading experts”, namely, experts that were best at some point in time. We derive regret bounds that depend only on this measure, independent of the total number of experts. We also consider a case where all experts remain grouped in just a few clusters in terms of their realized cumulative losses. Here too, our regret bounds depend only on the number of clusters determined in retrospect, which serves as a measure of complexity. Our results are obtained as special cases of a more general analysis for a setting of branching experts,where the set of experts may grow over time according to a tree-like structure, determined by an adversary. For this setting of branching experts, we give algorithms and analysis that cover both the full information and the bandit scenarios.

MOTIVATION: Many secretory proteins are synthesized as inactive precursors that must undergo post-translational proteolysis in order to mature and become active. In the current study, we address the challenge of sequence-based discovery of proteolytic sites in secreted proteins using machine learning. RESULTS: The results revealed that only half of the extracellular proteolytic sites are currently annotated, leaving over 3600 unannotated ones. Furthermore, we have found that only 6% of the unannotated sites are similar to known proteolytic sites, whereas the remaining 94% do not share significant similarity with any annotated proteolytic site. The computational challenges in these two cases are very different. While the precision in detecting the former group is close to perfect, only a mere 22% of the latter group were detected with a precision of 80%. The applicability of the classifier is demonstrated through members of the FGF family, in which we verified the conservation of physiologically-relevant proteolytic sites in homologous proteins.