arXiv subjects

Ravi Kumar

Publications and source records attributed to Ravi Kumar.

At least 109 records · Page 6Linked to original sources

arXiv2023

On User-Level Private Convex Optimization

We introduce a new mechanism for stochastic convex optimization (SCO) with user-level differential privacy guarantees. The convergence rates of this mechanism are similar to those in the prior work of Levy et al. (2021); Narayanan et al. (2022), but with two important improvements. Our mechanism does not require any smoothness assumptions on the loss. Furthermore, our bounds are also the first where the minimum number of users needed for user-level privacy has no dependence on the dimension and only a logarithmic dependence on the desired excess error. The main idea underlying the new mechanism is to show that the optimizers of strongly convex losses have low local deletion sensitivity, along with an output perturbation method for functions with low local deletion sensitivity, which could be of independent interest.

cs.LG↗

arXiv2023

Effect of Charge and Solvation Shell on Non-Radiative Decay Processes in s-Block Cationic Metal Ion Water Clusters

A molecular cluster's inner valence ionized state undergoes autoionization, which is nonlocal by nature. In a molecular system, when the inner valence's ionization potential (IP) is higher than the double ionization energy (DIP), it is energetically favorable for the initially ionized system to emit a secondary electron and reach a final state which is lower in energy. This relaxation usually happens via intermolecular coulombic decay (ICD) or electron transfer-mediated decay (ETMD). We have choosen the Na$^+$-(H$_2$O)$_{n=1-5}$ and Mg$^{2+}$-(H$_2$O)$_{m=1-5}$ cluster as the test systems. These systems are also found in the human body, which makes this study important. We have calculated the IP, DIP values, and the lifetime of Na-2s and Mg-2s temporary bound states (TBSs) in these clusters to study the effect of solvation on IP, DIP, and the lifetime of Na-2s and Mg-2s TBSs. We observe a considerable increase (96\%) in the lifetime of the Na-2s TBS in the second solvated shell structure in Na$^+$-(H$_ 2$O)$_{n=2}$ compared to the first solvated one. However, the increase in the lifetime of the Mg-2s state in the second solvation shell is only 33\%. We have revealed the different factors that affect the lifetime of TBSs and which type of decay process (ICD or ETMD) is dominant. We have shown how the charge of metal ions and increased water molecules affect the decay rate. We have shown that the decay of Mg-2p is also possible in all magnesium-water clusters, but it is not valid for the decay of Na-2p.

physics.chem-ph↗

arXiv2023

On Differentially Private Counting on Trees

We study the problem of performing counting queries at different levels in hierarchical structures while preserving individuals' privacy. Motivated by applications, we propose a new error measure for this problem by considering a combination of multiplicative and additive approximation to the query results. We examine known mechanisms in differential privacy (DP) and prove their optimality, under this measure, in the pure-DP setting. In the approximate-DP setting, we design new algorithms achieving significant improvements over known ones.

cs.DS↗

arXiv2023

Revenue Management without Demand Forecasting: A Data-Driven Approach for Bid Price Generation

Traditional revenue management relies on long and stable historical data and predictable demand patterns. However, meeting those requirements is not always possible. Many industries face demand volatility on an ongoing basis, an example would be air cargo which has much shorter booking horizon with highly variable batch arrivals. Even for passenger airlines where revenue management (RM) is well-established, reacting to external shocks is a well-known challenge that requires user monitoring and manual intervention. Moreover, traditional RM comes with strict data requirements including historical bookings and pricing even in the absence of any bookings, spanning multiple years. For companies that have not established a practice in RM, that type of extensive data is usually not available. We present a data-driven approach to RM which eliminates the need for demand forecasting and optimization techniques. We develop a methodology to generate bid prices using historical booking data only. Our approach is an ex-post greedy heuristic to estimate proxies for marginal opportunity costs as a function of remaining capacity and time-to-departure solely based on historical booking data. We utilize a neural network algorithm to project bid price estimations into the future. We conduct an extensive simulation study where we measure performance of our methodology compared to that of an optimally generated bid price using dynamic programming (DP). We also extend our simulations to measure performance of both data-driven and DP generated bid prices under the presence of demand misspecification. Our results show that our data-driven methodology stays near a theoretical optimum (<1% revenue gap) for a wide-range of settings, whereas DP deviates more significantly from the optimal as the magnitude of misspecification is increased. This highlights the robustness of our data-driven approach.

cs.LG↗

arXiv2022

Machine Learning based Framework for Robust Price-Sensitivity Estimation with Application to Airline Pricing

We consider the problem of dynamic pricing of a product in the presence of feature-dependent price sensitivity. Developing practical algorithms that can estimate price elasticities robustly, especially when information about no purchases (losses) is not available, to drive such automated pricing systems is a challenge faced by many industries. Based on the Poisson semi-parametric approach, we construct a flexible yet interpretable demand model where the price related part is parametric while the remaining (nuisance) part of the model is non-parametric and can be modeled via sophisticated machine learning (ML) techniques. The estimation of price-sensitivity parameters of this model via direct one-stage regression techniques may lead to biased estimates due to regularization. To address this concern, we propose a two-stage estimation methodology which makes the estimation of the price-sensitivity parameters robust to biases in the estimators of the nuisance parameters of the model. In the first-stage we construct estimators of observed purchases and prices given the feature vector using sophisticated ML estimators such as deep neural networks. Utilizing the estimators from the first-stage, in the second-stage we leverage a Bayesian dynamic generalized linear model to estimate the price-sensitivity parameters. We test the performance of the proposed estimation schemes on simulated and real sales transaction data from the Airline industry. Our numerical studies demonstrate that our proposed two-stage approach reduces the estimation error in price-sensitivity parameters from 25\% to 4\% in realistic simulation settings. The two-stage estimation techniques proposed in this work allows practitioners to leverage modern ML techniques to robustly estimate price-sensitivities while still maintaining interpretability and allowing ease of validation of its various constituent parts.

stat.ML↗

arXiv2022

Differentially Private Heatmaps

We consider the task of producing heatmaps from users' aggregated data while protecting their privacy. We give a differentially private (DP) algorithm for this task and demonstrate its advantages over previous algorithms on real-world datasets. Our core algorithmic primitive is a DP procedure that takes in a set of distributions and produces an output that is close in Earth Mover's Distance to the average of the inputs. We prove theoretical bounds on the error of our algorithm under a certain sparsity assumption and that these are near-optimal.

cs.DS↗

arXiv2022

Private Counting of Distinct and k-Occurring Items in Time Windows

In this work, we study the task of estimating the numbers of distinct and $k$-occurring items in a time window under the constraint of differential privacy (DP). We consider several variants depending on whether the queries are on general time windows (between times $t_1$ and $t_2$), or are restricted to being cumulative (between times $1$ and $t_2$), and depending on whether the DP neighboring relation is event-level or the more stringent item-level. We obtain nearly tight upper and lower bounds on the errors of DP algorithms for these problems. En route, we obtain an event-level DP algorithm for estimating, at each time step, the number of distinct items seen over the last $W$ updates with error polylogarithmic in $W$; this answers an open question of Bolot et al. (ICDT 2013).

cs.DS↗

arXiv2022

Private Isotonic Regression

In this paper, we consider the problem of differentially private (DP) algorithms for isotonic regression. For the most general problem of isotonic regression over a partially ordered set (poset) $\mathcal{X}$ and for any Lipschitz loss function, we obtain a pure-DP algorithm that, given $n$ input points, has an expected excess empirical risk of roughly $\mathrm{width}(\mathcal{X}) \cdot \log|\mathcal{X}| / n$, where $\mathrm{width}(\mathcal{X})$ is the width of the poset. In contrast, we also obtain a near-matching lower bound of roughly $(\mathrm{width}(\mathcal{X}) + \log |\mathcal{X}|) / n$, that holds even for approximate-DP algorithms. Moreover, we show that the above bounds are essentially the best that can be obtained without utilizing any further structure of the poset. In the special case of a totally ordered set and for $\ell_1$ and $\ell_2^2$ losses, our algorithm can be implemented in near-linear running time; we also provide extensions of this algorithm to the problem of private isotonic regression with additional structural constraints on the output function.

cs.LG↗

arXiv2022

Anonymized Histograms in Intermediate Privacy Models

We study the problem of privately computing the anonymized histogram (a.k.a. unattributed histogram), which is defined as the histogram without item labels. Previous works have provided algorithms with $\ell_1$- and $\ell_2^2$-errors of $O_\varepsilon(\sqrt{n})$ in the central model of differential privacy (DP). In this work, we provide an algorithm with a nearly matching error guarantee of $\tilde{O}_\varepsilon(\sqrt{n})$ in the shuffle DP and pan-private models. Our algorithm is very simple: it just post-processes the discrete Laplace-noised histogram! Using this algorithm as a subroutine, we show applications in privately estimating symmetric properties of distributions such as entropy, support coverage, and support size.

cs.DS↗

arXiv2022

Effect of Protonation and Deprotonation on Electron Transfer Mediated Decay and Interatomic Coulombic Decay

Electronically excited atoms or molecules in an environment are often subject to interatomic/intermolecular Coulombic decay (ICD) and/or electron transfer mediated decay (ETMD) mechanisms. A few of the numerous variables that can impact these non-radiative decay mechanisms include bond distance, the number of nearby atoms or molecules, and the polarisation effect. In this paper, we have studied the effect of protonation and deprotonation on the ionization potential (IP), double ionization potential (DIP), and lifetime (or decay width) of the temporary bound state in these non-radiative decay processes. We have chosen LiH-NH$_3$ and LiH-H$_2$O as test systems. The equation of motion coupled cluster singles and doubles method augmented by complex absorbing potential (CAP-EOM-CCSD) has been used in calculating the energetic position of the decaying state and the system's decay rate. Deprotonation of LiH-NH$_3$/LiH-H$_2$O either from the metal center (LiH) or from ammonia/water lowers the IP and DIP compared to the neutral systems. In contrast, protonation increases these quantities compared to neutral systems. The protonation closes the inner valence state relaxation channels for ICD/ETMD. For example, the decay of the O-2s/N-2s state stops in protonated systems (LiH$_2^+$-H$_2$O, LiH$_2^+$-NH$_3$, and LiH-NH$_4^+$). Our study also shows that the efficiency, i.e., the rate of ICD/ETMD, can be altered by protonation and deprotonation. It is expected to have implications for chemical and biological systems

physics.chem-ph↗

arXiv2022

Algorithms with More Granular Differential Privacy Guarantees

Differential privacy is often applied with a privacy parameter that is larger than the theory suggests is ideal; various informal justifications for tolerating large privacy parameters have been proposed. In this work, we consider partial differential privacy (DP), which allows quantifying the privacy guarantee on a per-attribute basis. In this framework, we study several basic data analysis and learning tasks, and design algorithms whose per-attribute privacy parameter is smaller that the best possible privacy parameter for the entire record of a person (i.e., all the attributes).

cs.CR↗

arXiv2022

Enhancement to Training of Bidirectional GAN : An Approach to Demystify Tax Fraud

Outlier detection is a challenging activity. Several machine learning techniques are proposed in the literature for outlier detection. In this article, we propose a new training approach for bidirectional GAN (BiGAN) to detect outliers. To validate the proposed approach, we train a BiGAN with the proposed training approach to detect taxpayers, who are manipulating their tax returns. For each taxpayer, we derive six correlation parameters and three ratio parameters from tax returns submitted by him/her. We train a BiGAN with the proposed training approach on this nine-dimensional derived ground-truth data set. Next, we generate the latent representation of this data set using the $encoder$ (encode this data set using the $encoder$) and regenerate this data set using the $generator$ (decode back using the $generator$) by giving this latent representation as the input. For each taxpayer, compute the cosine similarity between his/her ground-truth data and regenerated data. Taxpayers with lower cosine similarity measures are potential return manipulators. We applied our method to analyze the iron and steel taxpayers data set provided by the Commercial Taxes Department, Government of Telangana, India.

cs.LG↗

arXiv2022

Decay Processes in Cationic Alkali Metals in Microsolvated Clusters: A Complex Absorbing Potential Based Equation-of-Motion Coupled Cluster Investigation

We have employed the highly accurate complex absorbing potential based ionization potential equation-of-motion coupled cluster singles and doubles (CAP-IP-EOM-CCSD) method to study the various intermolecular decay processes in ionized metals (Li$^{+}$, Na$^{+}$, K$^{+}$) microsolvated by water molecules. For the Li atom, the electron is ionized from the 1s subshell. However, for Na and K atoms, the electron is ionized from 2s and both 2s and 2p subshells, respectively. We have investigated decay processes for the Li$^{+}$-(H$_{2}$O)$_{n}$; (n=1-3) systems as well as Na$^{+}$-(H$_{2}$O)$_{n}$; (n=1,2), and K$^{+}$-H$_{2}$O. The Lithium cation in water can decay only via electron transfer mediated decay (ETMD) as there are no valence electrons in Lithium. We have investigated how the various decay processes change in the presence of different alkali metal atoms and how the increasing number of water molecules play a significant role in the decay of microsolvated systems. To see the effect of the environment, we have studied the Li$^{+}$-NH$_{3}$ (in comparison to Li$^{+}$-H$_{2}$O). In the case of Na$^{+}$-H$_{2}$O, we have studied the impact of bond distance on the decay width. The effect of polarization on decay width is checked for the X$^{+}$-H$_{2}$O; X=Li, Na. We have used the PCM model to study the polarization effect. We have compared our results with the existing theoretical and experimental results wherever available in the literature.

physics.chem-ph↗

arXiv2022

Connect the Dots: Tighter Discrete Approximations of Privacy Loss Distributions

The privacy loss distribution (PLD) provides a tight characterization of the privacy loss of a mechanism in the context of differential privacy (DP). Recent work has shown that PLD-based accounting allows for tighter $(\varepsilon, δ)$-DP guarantees for many popular mechanisms compared to other known methods. A key question in PLD-based accounting is how to approximate any (potentially continuous) PLD with a PLD over any specified discrete support. We present a novel approach to this problem. Our approach supports both pessimistic estimation, which overestimates the hockey-stick divergence (i.e., $δ$) for any value of $\varepsilon$, and optimistic estimation, which underestimates the hockey-stick divergence. Moreover, we show that our pessimistic estimate is the best possible among all pessimistic estimates. Experimental evaluation shows that our approach can work with much larger discretization intervals while keeping a similar error bound compared to previous approaches and yet give a better approximation than existing methods.

cs.DS↗

arXiv2022

Faster Privacy Accounting via Evolving Discretization

We introduce a new algorithm for numerical composition of privacy random variables, useful for computing the accurate differential privacy parameters for composition of mechanisms. Our algorithm achieves a running time and memory usage of $\mathrm{polylog}(k)$ for the task of self-composing a mechanism, from a broad class of mechanisms, $k$ times; this class, e.g., includes the sub-sampled Gaussian mechanism, that appears in the analysis of differentially private stochastic gradient descent. By comparison, recent work by Gopi et al. (NeurIPS 2021) has obtained a running time of $\widetilde{O}(\sqrt{k})$ for the same task. Our approach extends to the case of composing $k$ different mechanisms in the same class, improving upon their running time and memory usage from $\widetilde{O}(k^{1.5})$ to $\widetilde{O}(k)$.

cs.DS↗

arXiv2022

Differentially Private All-Pairs Shortest Path Distances: Improved Algorithms and Lower Bounds

We study the problem of releasing the weights of all-pair shortest paths in a weighted undirected graph with differential privacy (DP). In this setting, the underlying graph is fixed and two graphs are neighbors if their edge weights differ by at most $1$ in the $\ell_1$-distance. We give an $ε$-DP algorithm with additive error $\tilde{O}(n^{2/3} / ε)$ and an $(ε, δ)$-DP algorithm with additive error $\tilde{O}(\sqrt{n} / ε)$ where $n$ denotes the number of vertices. This positively answers a question of Sealfon (PODS'16), who asked whether a $o(n)$-error algorithm exists. We also show that an additive error of $Ω(n^{1/6})$ is necessary for any sufficiently small $ε, δ> 0$. Finally, we consider a relaxed setting where a multiplicative approximation is allowed. We show that, with a multiplicative approximation factor $k$, %$2k - 1$, the additive error can be reduced to $\tilde{O}\left(n^{1/2 + O(1/k)} / ε\right)$ in the $ε$-DP case and $\tilde{O}(n^{1/3 + O(1/k)} / ε)$ in the $(ε, δ)$-DP case, respectively.

cs.DS↗

arXiv2022

Probing the electronic and local structure of Sr$_{2-x}$La$_x$CoNbO$_6$ using near-edge and extended x-ray absorption fine structures

We report the electronic and local structural investigation of double pervoskites Sr$_{2-x}$La$_x$CoNbO$_6$ ($x=$ 0--1) using x-ray absorption near edge structure (XANES) and extended x-ray absorption fine structures (EXAFS) at the Nb, Co, and Sr $K$-edges. The $ab$ $initio$ simulations and detailed analysis of the Nb and Co $K$-edge XANES spectra demonstrate that the observed pre-edge features arise from the transition of 1$s$ electrons to the mixed $p-d$ hybridized states. We reveal a $z$-out Jahn-Teller (JT) distortion in the CoO$_6$ octahedra, which decreases monotonically due to an enhancement in the JT inactive Co$^{2+}$ ions with $x$ . On the other hand, the $z$-in distortion in NbO$_6$ octahedra remains unaltered up to $x=$ 0.4 and then decreases with further increase in $x$. This sudden change in the local coordination around Nb atoms is found to be responsible for the evolution of the antiferromagnetic interactions in $x \geqslant$ 0.6 samples. Also, we establish a correlation between the degree of octahedral distortion and intensity of the white line feature in the XANES spectra and possible reason for this are discussed. More interestingly, we observe the signature of KN$_1$ double electron excitation in the Sr $K$-edge EXAFS spectra for all the samples, which is found to be in good agreement with the $Z$+1 approximation. Further, the Co L$_{2,3}$ edge shows the reduction in the crystal field strength and hence an increase in the charge transfer energy ($Δ_{ct}$) with the La substitution.

cond-mat.str-el↗

arXiv2022

Determination of topological edge quantum numbers of fractional quantum Hall phases

To determine the topological quantum numbers of fractional quantum Hall (FQH) states hosting counter-propagating (CP) downstream ($N_d$) and upstream ($N_u$) edge modes, it is pivotal to study quantized transport both in the presence and absence of edge mode equilibration. While reaching the non-equilibrated regime is challenging for charge transport, we target here the thermal Hall conductance $G_{Q}$, which is purely governed by edge quantum numbers $N_d$ and $N_u$. Our experimental setup is realized with a hBN encapsulated graphite gated monolayer graphene device. For temperatures up to $35mK$, our measured $G_{Q}$ at $ν= $ 2/3 and 3/5 (with CP modes) match the quantized values of non-equilibrated regime $(N_d + N_u)κ_{0}T$, where $κ_{0}T$ is a quanta of $G_{Q}$. With increasing temperature, $G_{Q}$ decreases and eventually takes the value of equilibrated regime $|N_d - N_u|κ_{0}T$. By contrast, at $ν= $1/3 and 2/5 (without CP modes), $G_Q$ remains robustly quantized at $N_dκ_{0}T$ independent of the temperature. Thus, measuring the quantized values of $G_{Q}$ at two regimes, we determine the edge quantum numbers, which opens a new route for finding the topological order of exotic non-Abelian FQH states.

cond-mat.mes-hall↗