Locally Decodable Codes (LDCs) are error-correcting codes for which individual message symbols can be quickly recovered despite errors in the codeword. LDCs for Hamming errors have been studied extensively in the past few decades, where a major goal is to understand the amount of redundancy that is necessary and sufficient to decode from large amounts of error, with small query complexity. In this work, we study LDCs for insertion and deletion errors, called Insdel LDCs. Their study was initiated by Ostrovsky and Paskin-Cherniavsky (Information Theoretic Security, 2015), who gave a reduction from Hamming LDCs to Insdel LDCs with a small blowup in the code parameters. On the other hand, the only known lower bounds for Insdel LDCs come from those for Hamming LDCs, thus there is no separation between them. Here we prove new, strong lower bounds for the existence of Insdel LDCs. In particular, we show that $2$-query linear Insdel LDCs do not exist, and give an exponential lower bound for the length of all $q$-query Insdel LDCs with constant $q$. For $q \ge 3$ our bounds are exponential in the existing lower bounds for Hamming LDCs. Furthermore, our exponential lower bounds continue to hold for adaptive decoders, and even in private-key settings where the encoder and decoder share secret randomness. This exhibits a strict separation between Hamming LDCs and Insdel LDCs. Our strong lower bounds also hold for the related notion of Insdel LCCs (except in the private-key setting), due to an analogue to the Insdel notions of a reduction from Hamming LCCs to LDCs. Our techniques are based on a delicate design and analysis of hard distributions of insertion and deletion errors, which depart significantly from typical techniques used in analyzing Hamming LDCs.
In machine learning, the selection of a promising model from a potentially large number of competing models and the assessment of its generalization performance are critical tasks that need careful consideration. Typically, model selection and evaluation are strictly separated endeavors, splitting the sample at hand into a training, validation, and evaluation set, and only compute a single confidence interval for the prediction performance of the final selected model. We however propose an algorithm how to compute valid lower confidence bounds for multiple models that have been selected based on their prediction performances in the evaluation set by interpreting the selection problem as a simultaneous inference problem. We use bootstrap tilting and a maxT-type multiplicity correction. The approach is universally applicable for any combination of prediction models, any model selection strategy, and any prediction performance measure that accepts weights. We conducted various simulation experiments which show that our proposed approach yields lower confidence bounds that are at least comparably good as bounds from standard approaches, and that reliably reach the nominal coverage probability. In addition, especially when sample size is small, our proposed approach yields better performing prediction models than the default selection of only one model for evaluation does.
This article considers linear approximation based on function evaluations in reproducing kernel Hilbert spaces of the Gaussian kernel and a more general class of weighted power series kernels on the interval $[-1, 1]$. We derive almost matching upper and lower bounds on the worst-case error, measured both in the uniform and $L^2([-1,1])$-norm, in these spaces. The results show that if the power series kernel expansion coefficients $\alpha_n^{-1}$ decay at least factorially, their rate of decay controls that of the worst-case error. Specifically, (i) the $n$th minimal error decays as $\alpha_n^{{ -1/2}}$ up to a sub-exponential factor and (ii) for any $n$ sampling points in $[-1, 1]$ there exists a linear algorithm whose error is $\alpha_n^{{ -1/2}}$ up to an exponential factor. For the Gaussian kernel the dominating factor in the bounds is $(n!)^{-1/2}$.
Many organizations run thousands of randomized experiments, or A/B tests, to statistically quantify and detect the impact of product changes. Analysts take these results to augment decision-making around deployment and investment opportunities, making the time it takes to detect an effect a key priority. Often, these experiments are conducted on customers arriving sequentially; however, the analysis is only performed at the end of the study. This is undesirable because strong effects can be detected before the end of the study, which is especially relevant for risk mitigation when the treatment effect is negative. Alternatively, analysts could perform hypotheses tests more frequently and stop the experiment when the estimated causal effect is statistically significant; this practice is often called "peeking." Unfortunately, peeking invalidates the statistical guarantees and quickly leads to a substantial uncontrolled type-1 error. Our paper provides valid confidence sequences from the design-based perspective, where we condition on the full set of potential outcomes and perform inference on the obtained sample. Our design-based confidence sequence accommodates a wide variety of sequential experiments in an assumption-light manner. In particular, we build confidence sequences for 1) the average treatment effect for different individuals arriving sequentially, 2) the reward mean difference in multi-arm bandit settings with adaptive treatment assignments, 3) the contemporaneous treatment effect for single time series experiment with potential carryover effects in the potential outcome, and 4) the average contemporaneous treatment effect in panel experiments. We further provide a variance reduction technique that incorporates modeling assumptions and covariates to reduce the confidence sequence width proportional to how well the analyst can predict the next outcome.
Streaming keyword spotting is a widely used solution for activating voice assistants. Deep Neural Networks with Hidden Markov Model (DNN-HMM) based methods have proven to be efficient and widely adopted in this space, primarily because of the ability to detect and identify the start and end of the wake-up word at low compute cost. However, such hybrid systems suffer from loss metric mismatch when the DNN and HMM are trained independently. Sequence discriminative training cannot fully mitigate the loss-metric mismatch due to the inherent Markovian style of the operation. We propose an low footprint CNN model, called HEiMDaL, to detect and localize keywords in streaming conditions. We introduce an alignment-based classification loss to detect the occurrence of the keyword along with an offset loss to predict the start of the keyword. HEiMDaL shows 73% reduction in detection metrics along with equivalent localization accuracy and with the same memory footprint as existing DNN-HMM style models for a given wake-word.
We give a simplified and improved lower bound for the simplex range reporting problem. We show that given a set $P$ of $n$ points in $\mathbb{R}^d$, any data structure that uses $S(n)$ space to answer such queries must have $Q(n)=\Omega((n^2/S(n))^{(d-1)/d}+k)$ query time, where $k$ is the output size. For near-linear space data structures, i.e., $S(n)=O(n\log^{O(1)}n)$, this improves the previous lower bounds by Chazelle and Rosenberg [CR96] and Afshani [A12] but perhaps more importantly, it is the first ever tight lower bound for any variant of simplex range searching for $d\ge 3$ dimensions. We obtain our lower bound by making a simple connection to well-studied problems in incident geometry which allows us to use known constructions in the area. We observe that a small modification of a simple already existing construction can lead to our lower bound. We believe that our proof is accessible to a much wider audience, at least compared to the previous intricate probabilistic proofs based on measure arguments by Chazelle and Rosenberg [CR96] and Afshani [A12]. The lack of tight or almost-tight (up to polylogarithmic factor) lower bounds for near-linear space data structures is a major bottleneck in making progress on problems such as proving lower bounds for multilevel data structures. It is our hope that this new line of attack based on incidence geometry can lead to further progress in this area.
An important issue in medical image processing is to be able to estimate not only the performances of algorithms but also the precision of the estimation of these performances. Reporting precision typically amounts to reporting standard-error of the mean (SEM) or equivalently confidence intervals. However, this is rarely done in medical image segmentation studies. In this paper, we aim to estimate what is the typical confidence that can be expected in such studies. To that end, we first perform experiments for Dice metric estimation using a standard deep learning model (U-net) and a classical task from the Medical Segmentation Decathlon. We extensively study precision estimation using both Gaussian assumption and bootstrapping (which does not require any assumption on the distribution). We then perform simulations for other test set sizes and performance spreads. Overall, our work shows that small test sets lead to wide confidence intervals ($\sim$6 points of Dice for 20 samples) and that, in order to obtain a confidence interval narrower than 2, it is necessary to have at least 200 test samples.
Adaptive experimental design methods are increasingly being used in industry as a tool to boost testing throughput or reduce experimentation cost relative to traditional A/B/N testing methods. This paper shares lessons learned regarding the challenges and pitfalls of naively using adaptive experimentation systems in industrial settings where non-stationarity is prevalent, while also providing perspectives on the proper objectives and system specifications in these settings. We developed an adaptive experimental design framework for counterfactual inference based on these experiences, and tested it in a commercial environment.
Many language tasks (e.g., Named Entity Recognition, Part-of-Speech tagging, and Semantic Role Labeling) are naturally framed as sequence tagging problems. However, there has been comparatively little work on interpretability methods for sequence tagging models. In this paper, we extend influence functions - which aim to trace predictions back to the training points that informed them - to sequence tagging tasks. We define the influence of a training instance segment as the effect that perturbing the labels within this segment has on a test segment level prediction. We provide an efficient approximation to compute this, and show that it tracks with the true segment influence, measured empirically. We show the practical utility of segment influence by using the method to identify systematic annotation errors in two named entity recognition corpora. Code to reproduce our results is available at //github.com/successar/Segment_Influence_Functions.
We introduce and analyse an efficient decoder for the quantum Tanner codes of that can correct adversarial errors of linear weight. Previous decoders for quantum low-density parity-check codes could only handle adversarial errors of weight $O(\sqrt{n \log n})$. We also work on the link between quantum Tanner codes and the Lifted Product codes of Panteleev and Kalachev, and show that our decoder can be adapted to the latter. The decoding algorithm alternates between sequential and parallel procedures and converges in linear time.
The overheads of classical decoding for quantum error correction on superconducting quantum systems grow rapidly with the number of logical qubits and their correction code distance. Decoding at room temperature is bottle-necked by refrigerator I/O bandwidth while cryogenic on-chip decoding is limited by area/power/thermal budget. To overcome these overheads, we are motivated by the observation that in the common case, error signatures are fairly trivial with high redundancy/sparsity, since the error correction codes are over-provisioned to correct for uncommon worst-case complex scenarios (to ensure substantially low logical error rates). If suitably exploited, these trivial signatures can be decoded and corrected with insignificant overhead, thereby alleviating the bottlenecks described above, while still handling the worst-case complex signatures by state-of-the-art means. Our proposal, targeting Surface Codes, consists of: 1) Clique: A lightweight decoder for decoding and correcting trivial common-case errors, designed for the cryogenic domain. The decoder is implemented for SFQ logic. 2) A statistical confidence-based technique for off-chip decoding bandwidth allocation, to efficiently handle rare complex decodes which are not covered by the on-chip decoder. 3) A method for stalling circuit execution, for the worst-case scenarios in which the provisioned off-chip bandwidth is insufficient to complete all requested off-chip decodes. In all, our proposal enables 70-99+% off-chip bandwidth elimination across a range of logical and physical error rates, without significantly sacrificing the accuracy of state-of-the-art off-chip decoding. By doing so, it achieves 10-10000x bandwidth reduction over prior off-chip bandwidth reduction techniques. Furthermore, it achieves a 15-37x resource overhead reduction compared to prior on-chip-only decoding.