arXiv subjects

Shikha Singh

Publications and source records attributed to Shikha Singh.

At least 19 recordsLinked to original sources

arXiv2026

Incremental Strongly Connected Components with Predictions

Algorithms with predictions is a growing area that aims to leverage machine-learned predictions to design faster beyond-worst-case algorithms. In this paper, we use this framework to design a learned data structure for the incremental strongly connected components (SCC) problem. In this problem, the $n$ vertices of a graph are known a priori and the $m$ directed edges arrive over time. The goal is to efficiently maintain the strongly connected components of the graph after each insert. Our algorithm receives a possibly erroneous prediction of the edge sequence and uses it to precompute partial solutions to support fast inserts. We show that our algorithm achieves nearly optimal bounds with good predictions and its performance smoothly degrades with the prediction error. We also implement our data structure and perform experiments on real datasets. Our empirical results show that the theory is predictive of practical runtime improvements.

cs.DS↗

arXiv2026

Stable Matching with Predictions: Robustness and Efficiency under Pruned Preferences

In this paper, we study the fundamental problem of finding a stable matching in two-sided matching markets. In the classic variant, it is assumed that both sides of the market submit a ranked list of all agents on the other side. However, in large matching markets such as the National Resident Matching Program (NRMP), it is infeasible for hospitals to interview or mutually rank each resident. In this paper, we study the stable matching problem with truncated preference lists. In particular, we assume that, based on historical datasets, each hospital has a predicted rank of its likely match and only ranks residents within a bounded interval around that prediction. We use the algorithms-with-predictions framework and show that the classic deferred-acceptance (DA) algorithm used to compute stable matchings is robust to such truncation. We present two algorithms and theoretically and empirically evaluate their performance. Our results show that even with reasonably accurate predictions, it is possible to significantly cut down on both instance size (the length of preference lists) as well as the number of proposals made. These results explain the practical success of the DA algorithm and connect market design to the emerging theory of algorithms with predictions.

cs.GT↗

arXiv2025

Incremental Approximate Single-Source Shortest Paths with Predictions

The algorithms-with-predictions framework has been used extensively to develop online algorithms with improved beyond-worst-case competitive ratios. Recently, there is growing interest in leveraging predictions for designing data structures with improved beyond-worst-case running times. In this paper, we study the fundamental data structure problem of maintaining approximate shortest paths in incremental graphs in the algorithms-with-predictions model. Given a sequence $σ$ of edges that are inserted one at a time, the goal is to maintain approximate shortest paths from the source to each vertex in the graph at each time step. Before any edges arrive, the data structure is given a prediction of the online edge sequence $\hatσ$ which is used to ``warm start'' its state. As our main result, we design a learned algorithm that maintains $(1+ε)$-approximate single-source shortest paths, which runs in $\tilde{O}(m η\log W/ε)$ time, where $W$ is the weight of the heaviest edge and $η$ is the prediction error. We show these techniques immediately extend to the all-pairs shortest-path setting as well. Our algorithms are consistent (performing nearly as fast as the offline algorithm) when predictions are nearly perfect, have a smooth degradation in performance with respect to the prediction error and, in the worst case, match the best offline algorithm up to logarithmic factors. As a building block, we study the offline incremental approximate single-source shortest-paths problem. In this problem, the edge sequence $σ$ is known a priori and the goal is to efficiently return the length of the shortest paths in the intermediate graph $G_t$ consisting of the first $t$ edges, for all $t$. Note that the offline incremental problem is defined in the worst-case setting (without predictions) and is of independent interest.

cs.DS↗

arXiv2024

Incremental Topological Ordering and Cycle Detection with Predictions

This paper leverages the framework of algorithms-with-predictions to design data structures for two fundamental dynamic graph problems: incremental topological ordering and cycle detection. In these problems, the input is a directed graph on $n$ nodes, and the $m$ edges arrive one by one. The data structure must maintain a topological ordering of the vertices at all times and detect if the newly inserted edge creates a cycle. The theoretically best worst-case algorithms for these problems have high update cost (polynomial in $n$ and $m$). In practice, greedy heuristics (that recompute the solution from scratch each time) perform well but can have high update cost in the worst case. In this paper, we bridge this gap by leveraging predictions to design a learned new data structure for the problems. Our data structure guarantees consistency, robustness, and smoothness with respect to predictions -- that is, it has the best possible running time under perfect predictions, never performs worse than the best-known worst-case methods, and its running time degrades smoothly with the prediction error. Moreover, we demonstrate empirically that predictions, learned from a very small training dataset, are sufficient to provide significant speed-ups on real datasets.

cs.DS↗

arXiv2024

Unbalanced Random Matching Markets with Partial Preferences

Properties of stable matchings in the popular random-matching-market model have been studied for over 50 years. In a random matching market, each agent has complete preferences drawn uniformly and independently at random. Wilson (1972), Knuth (1976) and Pittel (1989) proved that in balanced random matching markets, the proposers are matched to their $\ln n$th choice on average. In this paper, we consider markets where agents have partial (truncated) preferences, that is, the proposers only rank their top $d$ partners. Despite the long history of the problem, the following fundamental question remained unanswered: \emph{what is the smallest value of $d$ that results in a perfect stable matching with high probability?} In this paper, we answer this question exactly -- we prove that a degree of $\ln^2 n$ is necessary and sufficient. That is, we show that if $d < (1-ε) \ln^2 n$ then no stable matching is perfect and if $d > (1+ ε) \ln^2 n$, then every stable matching is perfect with high probability. This settles a recent conjecture by Kanoria, Min and Qian (2021). We generalize this threshold for unbalanced markets: we consider a matching market with $n$ agents on the shorter side and $n(α+1)$ agents on the longer side. We show that for markets with $α=o(1)$, the sharp threshold characterizing the existence of perfect stable matching occurs when $d$ is $\ln n \cdot \ln \left(\frac{1 + α}{α+ (1/n(α+1))} \right)$. Finally, we extend the line of work studying the effect of imbalance on the expected rank of the proposers (termed the ``stark effect of competition''). We establish the regime in unbalanced markets that forces this stark effect to take shape in markets with partial preferences.

cs.GT↗

arXiv2023

Online List Labeling with Predictions

A growing line of work shows how learned predictions can be used to break through worst-case barriers to improve the running time of an algorithm. However, incorporating predictions into data structures with strong theoretical guarantees remains underdeveloped. This paper takes a step in this direction by showing that predictions can be leveraged in the fundamental online list labeling problem. In the problem, n items arrive over time and must be stored in sorted order in an array of size Theta(n). The array slot of an element is its label and the goal is to maintain sorted order while minimizing the total number of elements moved (i.e., relabeled). We design a new list labeling data structure and bound its performance in two models. In the worst-case learning-augmented model, we give guarantees in terms of the error in the predictions. Our data structure provides strong guarantees: it is optimal for any prediction error and guarantees the best-known worst-case bound even when the predictions are entirely erroneous. We also consider a stochastic error model and bound the performance in terms of the expectation and variance of the error. Finally, the theoretical results are demonstrated empirically. In particular, we show that our data structure has strong performance on real temporal data sets where predictions are constructed from elements that arrived in the past, as is typically done in a practical use case.

cs.DS↗

arXiv2023

FlashBench: A lightning nowcasting framework based on the hybrid deep learning and physics-based dynamical models

Lightning strikes are a well-known danger, and are a leading cause of accidental fatality worldwide. Unfortunately, lightning hazards seldom make headlines in international media coverage because of their infrequency and the low number of casualties each incidence. According to readings from the TRMM LIS lightning sensor, thunderstorms are more common in the tropics while being extremely rare in the polar regions. To improve the precision of lightning forecasts, we develop a technique similar to LightNet's, with one key modification. We didn't just base our model off the results of preliminary numerical simulations; we also factored in the observed fields' time-dependent development. The effectiveness of the lightning forecast rose dramatically once this adjustment was made. The model was tested in a case study during a thunderstorm. Using lightning parameterization in the WRF model simulation, we compared the simulated fields. As the first of its type, this research has the potential to set the bar for how regional lightning predictions are conducted in the future because of its data-driven approach. In addition, we have built a cloud-based lightning forecast system based on Google Earth Engine. With this setup, lightning forecasts over West India may be made in real time, giving critically important information for the area.

physics.ao-ph↗

arXiv2023

Changing agents and ascribing beliefs in dynamic epistemic logic

In dynamic epistemic logic (Van Ditmarsch, Van Der Hoek, & Kooi, 2008) it is customary to use an action frame (Baltag & Moss, 2004; Baltag, Moss, & Solecki, 1998) to describe different views of a single action. In this article, action frames are extended to add or remove agents, we call these agent-update frames. This can be done selectively so that only some specified agents get information of the update, which can be used to model several interesting examples such as private update and deception, studied earlier by Baltag and Moss (2004); Sakama (2015); Van Ditmarsch, Van Eijck, Sietsma, and Wang (2012). The product update of a Kripke model by an action frame is an abbreviated way of describing the transformed Kripke model which is the result of performing the action. This is substantially extended to a sum-product update of a Kripke model by an agent-update frame in the new setting. These ideas are applied to an AI problem of modelling a story. We show that dynamic epistemic logics, with update modalities now based on agent-update frames, continue to have sound and complete proof systems. Decision procedures for model checking and satisfiability have expected complexity. For a sublanguage, there are polynomial space algorithms.

cs.AI↗

arXiv2021

Non-Cooperative Rational Interactive Proofs

Interactive-proof games model the scenario where an honest party interacts with powerful but strategic provers, to elicit from them the correct answer to a computational question. Interactive proofs are increasingly used as a framework to design protocols for computation outsourcing. Existing interactive-proof games largely fall into two categories: either as games of cooperation such as multi-prover interactive proofs and cooperative rational proofs, where the provers work together as a team; or as games of conflict such as refereed games, where the provers directly compete with each other in a zero-sum game. Neither of these extremes truly capture the strategic nature of service providers in outsourcing applications. How to design and analyze non-cooperative interactive proofs is an important open problem. In this paper, we introduce a mechanism-design approach to define a multi-prover interactive-proof model in which the provers are rational and non-cooperative---they act to maximize their expected utility given others' strategies. We define a strong notion of backwards induction as our solution concept to analyze the resulting extensive-form game with imperfect information. Our protocols provide utility gap guarantees, which are analogous to soundness gap in classic interactive proofs. At a high level, a utility gap of u means that the protocol is robust against provers that may not care about a utility loss of 1/u. We fully characterize the complexity of our proof system under different utility gap guarantees. For example, we show that with a polynomial utility gap, the power of non-cooperative rational interactive proofs is exactly P^NEXP.

cs.GT↗

arXiv2021

Telescoping Filter: A Practical Adaptive Filter

Filters are fast, small and approximate set membership data structures. They are often used to filter out expensive accesses to a remote set S for negative queries (that is, a query x not in S). Filters have one-sided errors: on a negative query, a filter may say "present" with a tunable false-positve probability of epsilon. Correctness is traded for space: filters only use log (1/ε) + O(1) bits per element. The false-positive guarantees of most filters, however, hold only for a single query. In particular, if x is a false positive of a filter, a subsequent query to x is a false positive with probability 1, not epsilon. With this in mind, recent work has introduced the notion of an adaptive filter. A filter is adaptive if each query has false positive epsilon, regardless of what queries were made in the past. This requires "fixing" false positives as they occur. Adaptive filters not only provide strong false positive guarantees in adversarial environments but also improve performance on query practical workloads by eliminating repeated false positives. Existing work on adaptive filters falls into two categories. First, there are practical filters based on cuckoo filters that attempt to fix false positives heuristically, without meeting the adaptivity guarantee. Meanwhile, the broom filter is a very complex adaptive filter that meets the optimal theoretical bounds. In this paper, we bridge this gap by designing a practical, provably adaptive filter: the telescoping adaptive filter. We provide theoretical false-positive and space guarantees of our filter, along with empirical results where we compare its false positive performance against state-of-the-art filters. We also test the throughput of our filters, showing that they achieve comparable performance to similar non-adaptive filters.

cs.DS↗

arXiv2020

Subjective Knowledge and Reasoning about Agents in Multi-Agent Systems

Though a lot of work in multi-agent systems is focused on reasoning about knowledge and beliefs of artificial agents, an explicit representation and reasoning about the presence/absence of agents, especially in the scenarios where agents may be unaware of other agents joining in or going offline in a multi-agent system, leading to partial knowledge/asymmetric knowledge of the agents is mostly overlooked by the MAS community. Such scenarios lay the foundations of cases where an agent can influence other agents' mental states by (mis)informing them about the presence/absence of collaborators or adversaries. In this paper, we investigate how Kripke structure-based epistemic models can be extended to express the above notion based on an agent's subjective knowledge and we discuss the challenges that come along.

cs.MA↗

arXiv2019

Non-intrusive Load Monitoring via Multi-label Sparse Representation based Classification

This work follows the approach of multi-label classification for non-intrusive load monitoring (NILM). We modify the popular sparse representation based classification (SRC) approach (developed for single label classification) to solve multi-label classification problems. Results on benchmark REDD and Pecan Street dataset shows significant improvement over state-of-the-art techniques with small volume of training data.

eess.SP↗

arXiv2019

Deep Sparse Coding for Non-Intrusive Load Monitoring

Energy disaggregation is the task of segregating the aggregate energy of the entire building (as logged by the smartmeter) into the energy consumed by individual appliances. This is a single channel (the only channel being the smart-meter) blind source (different electrical appliances) separation problem. The traditional way to address this is via stochastic finite state machines (e.g. Factorial Hidden Markov Model). In recent times dictionary learning based approaches have shown promise in addressing the disaggregation problem. The usual technique is to learn a dictionary for every device and use the learnt dictionaries as basis for blind source separation during disaggregation. Prior studies in this area are shallow learning techniques, i.e. they learn a single layer of dictionary for every device. In this work, we propose a deep learning approach, instead of learning one level of dictionary, we learn multiple layers of dictionaries for each device. These multi-level dictionaries are used as a basis for source separation during disaggregation. Results on two benchmark datasets and one actual implementation show that our method outperforms state-of-the-art techniques.

eess.SP↗

arXiv2019

Analysis Co-Sparse Coding for Energy Disaggregation

Energy disaggregation is the task of segregating the aggregate energy of the entire building (as logged by the smartmeter) into the energy consumed by individual appliances. This is a single channel (the only channel being the smart-meter) blind source (different electrical appliances) separation problem. In recent times dictionary learning based approaches have shown promise in addressing the disaggregation problem. The usual technique is to learn a dictionary for every device and use the learnt dictionaries as basis for blind source separation during disaggregation. Dictionary learning is a synthesis formulation; in this work, we propose an analysis approach. The advantage of our proposed approach is that, the requirement of training volume drastically reduces compared to state-of-the-art techniques. This means that, we require fewer instrumented homes, or fewer days of instrumentation per home; in either case this drastically reduces the sensing cost. Results on two benchmark datasets show that our method produces the same level of disaggregation accuracy as state-of-the-art methods but with only a fraction of the training data.

eess.SP↗

arXiv2019

Multi Label Restricted Boltzmann Machine for Non-Intrusive Load Monitoring

Increasing population indicates that energy demands need to be managed in the residential sector. Prior studies have reflected that the customers tend to reduce a significant amount of energy consumption if they are provided with appliance-level feedback. This observation has increased the relevance of load monitoring in today's tech-savvy world. Most of the previously proposed solutions claim to perform load monitoring without intrusion, but they are not completely non-intrusive. These methods require historical appliance-level data for training the model for each of the devices. This data is gathered by putting a sensor on each of the appliances present in the home which causes intrusion in the building. Some recent studies have proposed that if we frame Non-Intrusive Load Monitoring (NILM) as a multi-label classification problem, the need for appliance-level data can be avoided. In this paper, we propose Multi-label Restricted Boltzmann Machine(ML-RBM) for NILM and report an experimental evaluation of proposed and state-of-the-art techniques.

cs.LG↗

arXiv2018

The Online Event-Detection Problem

Given a stream $S = (s_1, s_2, ..., s_N)$, a $ϕ$-heavy hitter is an item $s_i$ that occurs at least $ϕN$ times in $S$. The problem of finding heavy-hitters has been extensively studied in the database literature. In this paper, we study a related problem. We say that there is a $ϕ$-event at time $t$ if $s_t$ occurs exactly $ϕN$ times in $(s_1, s_2, ..., s_t)$. Thus, for each $ϕ$-heavy hitter there is a single $ϕ$-event which occurs when its count reaches the reporting threshold $ϕN$. We define the online event-detection problem (OEDP) as: given $ϕ$ and a stream $S$, report all $ϕ$-events as soon as they occur. Many real-world monitoring systems demand event detection where all events must be reported (no false negatives), in a timely manner, with no non-events reported (no false positives), and a low reporting threshold. As a result, the OEDP requires a large amount of space (Omega(N) words) and is not solvable in the streaming model or via standard sampling-based approaches. Since OEDP requires large space, we focus on cache-efficient algorithms in the external-memory model. We provide algorithms for the OEDP that are within a log factor of optimal. Our algorithms are tunable: its parameters can be set to allow for a bounded false-positives and a bounded delay in reporting. None of our relaxations allow false negatives since reporting all events is a strict requirement of our applications. Finally, we show improved results when the count of items in the input stream follows a power-law distribution.

cs.DS↗

arXiv2018

Efficient Rational Proofs with Strong Utility-Gap Guarantees

As modern computing moves towards smaller devices and powerful cloud platforms, more and more computation is being delegated to powerful service providers. Interactive proofs are a widely-used model to design efficient protocols for verifiable computation delegation. Rational proofs are payment-based interactive proofs. The payments are designed to incentivize the provers to give correct answers. If the provers misreport the answer then they incur a payment loss of at least 1/u, where u is the utility gap of the protocol. In this work, we tightly characterize the power of rational proofs that are super efficient, that is, require only logarithmic time and communication for verification. We also characterize the power of single-round rational protocols that require only logarithmic space and randomness for verification. Our protocols have strong (that is, polynomial, logarithmic, and even constant) utility gap. Finally, we show when and how rational protocols can be converted to give the completeness and soundness guarantees of classical interactive proofs.

cs.GT↗

arXiv2018

Bloom Filters, Adaptivity, and the Dictionary Problem

The Bloom filter---or, more generally, an approximate membership query data structure (AMQ)---maintains a compact, probabilistic representation of a set S of keys from a universe U. An AMQ supports lookups, inserts, and (for some AMQs) deletes. A query for an x in S is guaranteed to return "present." A query for x not in S returns "absent" with probability at least 1-epsilon, where epsilon is a tunable false positive probability. If a query returns "present," but x is not in S, then x is a false positive of the AMQ. Because AMQs have a nonzero probability of false-positives, they require far less space than explicit set representations. AMQs are widely used to speed up dictionaries that are stored remotely (e.g., on disk/across a network). Most AMQs offer weak guarantees on the number of false positives they will return on a sequence of queries. The false-positive probability of epsilon holds only for a single query. It is easy for an adversary to drive an AMQ's false-positive rate towards 1 by simply repeating false positives. This paper shows what it takes to get strong guarantees on the number of false positives. We say that an AMQs is adaptive if it guarantees a false-positive probability of epsilon for every query, regardless of answers to previous queries. First, we prove that it is impossible to build a small adaptive AMQ, even when the AMQ is immediately told whenever it returns a false positive. We then show how to build an adaptive AMQ that partitions its state into a small local component and a larger remote component. In addition to being adaptive, the local component of our AMQ dominates existing AMQs in all regards. It uses optimal space up to lower-order terms and supports queries and updates in worst-case constant time, with high probability. Thus, we show that adaptivity has no cost.

cs.DS↗