Probabilistic Computation Research Articles

Deliberate underpricing and after-market mispricing in Indian IPO market: Stochastic frontier approach

Purpose This paper aims to study the underpricing phenomenon of initial public offerings (IPOs) of 355 Indian companies issued from 2007 to 2019. The research question this paper empirically examines is whether Indian corporate executives deliberately underprice IPOs from its fair value to attract investors, thereby causing an abnormal spike in the prices on the listing day. The findings of this study challenge a commonly held notion of leaving money on the table by IPO issuing companies. Of the overall average listing day returns of 17%, the deliberate premarket underpricing component is found to be mere 5.3%, while the remaining price fluctuation is, inter alia, a result of market momentum along with the unmet demands of impatient investors. Design/methodology/approach Following Koop and Li (2001), this study uses Stochastic frontier model (SFM) to study a routine anomaly of disparity between the primary market price (i.e. IPO issue price) and the secondary market price (listing price). The jump in the issue price observed on a listing day is decomposed into deliberate premarket underpricing component that reflects the extent of managerial manipulation and the after-market misvaluation component attributable to information asymmetry and prevailing market volatility. Findings This paper uses SFM to bifurcate initial returns into deliberate underpricing by managers and after-market mispricing by noise traders. This study finds that a significant part of the initial return is explained through after-market mispricing. This study finds that average initial returns are 17%, deliberate premarket underpricing is 5.3% and after-market mispricing averages 11.9%. Research limitations/implications This study can isolate underpricing done at the premarket by estimating a systematic one-sided error term that measures the maximum predicted issue price deviation from the offered price. Consequentially, the disaggregation of initial returns may be especially informative for retail investors in planning their exit strategy from an IPO by separating the strength of the firm's fundamentals and its causal relationship with the initial returns. Substantial proportion of after-market mispricing implies that future research should focus on factors causing after-market mispricing. As underlying causes are identified, tailor-made policy responses can be formulated to benefit investors. Practical implications This paper has empirically validated that initial return is a mix of both components, i.e. deliberate underpricing and aftermarket mispricing. This disaggregation of initial returns can prove helpful for investors in planning their exit strategy. This study can help investors to become more aware of the importance of the fundamentals of the firm and its causal relation with the initial returns. This information in turn can help reduce the information asymmetry amongst investors and help them lessen the costs of adverse selection. Originality/value A large number of research studies on IPO pricing find overwhelming evidence of underpricing in public issues. This research attempts to decompose the extent of underpricing into deliberate underpricing and after-market mispricing, thereby supplementing the existing literature on the IPO pricing puzzle. To the best of the authors’ knowledge, this study is the first contribution to the literature on initial return decomposition for the Indian capital markets.

Mobile agent path planning under uncertain environment using reinforcement learning and probabilistic model checking

The major challenge in mobile agent path planning, within an uncertain environment, is effectively determining an optimal control model to discover the target location as quickly as possible and evaluating the control system’s reliability. To address this challenge, we introduce a learning-verification integrated mobile agent path planning method to achieve both the effectiveness and the reliability. More specifically, we first propose a modified Q-learning algorithm (a popular reinforcement learning algorithm), called QEA−learning algorithm, to find the best Q-table in the environment. We then determine the location transition probability matrix, and establish a probability model using the assumption that the agent selects a location with a higher Q-value. Secondly, the learnt behaviour of the mobile agent based on QEA−learning algorithm, is formalized as a Discrete-time Markov Chain (DTMC) model. Thirdly, the required reliability requirements of the mobile agent control system are specified using Probabilistic Computation Tree Logic (PCTL). In addition, the DTMC model and the specified properties are taken as the input of the Probabilistic Model Checker PRISM for automatic verification. This is preformed to evaluate and verify the control system’s reliability. Finally, a case study of a mobile agent walking in a grids map is used to illustrate the proposed learning algorithm. Here we have a special focus on the modelling approach demonstrating how PRISM can be used to analyse and evaluate the reliability of the mobile agent control system learnt via the proposed algorithm. The results show that the path identified using the proposed integrated method yields the largest expected reward.

Distance problems within Helly graphs and k-Helly graphs

The ball hypergraph of a graph G is the family of balls of all possible centers and radii in G. Balls in a subfamily are k-wise intersecting if the intersection of any k balls in the subfamily is always nonempty. The Helly number of a ball hypergraph is the least integer k greater than one such that every subfamily of k-wise intersecting balls has a nonempty common intersection. A graph is k-Helly (or Helly, if k=2) if its ball hypergraph has Helly number at most k. We prove that a central vertex and all the medians in an n-vertex m-edge Helly graph can be computed w.h.p. in O˜(mn) time. Both results extend to a broader setting where we assign a nonnegative cost to the vertices. For any fixed k, we also present an O˜(mkn)-time randomized algorithm for radius computation within k-Helly graphs. If we relax the definition of Helly number (for what is sometimes called an “almost Helly-type” property in the literature), then our approach leads to an approximation algorithm for computing the radius with an additive one-sided error of at most some constant.

ADEV: Sound Automatic Differentiation of Expected Values of Probabilistic Programs

Optimizing the expected values of probabilistic processes is a central problem in computer science and its applications, arising in fields ranging from artificial intelligence to operations research to statistical computing. Unfortunately, automatic differentiation techniques developed for deterministic programs do not in general compute the correct gradients needed for widely used solutions based on gradient-based optimization. In this paper, we present ADEV, an extension to forward-mode AD that correctly differentiates the expectations of probabilistic processes represented as programs that make random choices. Our algorithm is a source-to-source program transformation on an expressive, higher-order language for probabilistic computation, with both discrete and continuous probability distributions. The result of our transformation is a new probabilistic program, whose expected return value is the derivative of the original program’s expectation. This output program can be run to generate unbiased Monte Carlo estimates of the desired gradient, that can be used within the inner loop of stochastic gradient descent. We prove ADEV correct using logical relations over the denotations of the source and target probabilistic programs. Because it modularly extends forward-mode AD, our algorithm lends itself to a concise implementation strategy, which we exploit to develop a prototype in just a few dozen lines of Haskell (https://github.com/probcomp/adev).

Probabilistic computations of virial coefficients of polymeric structures described by rigid configurations of spherical particles: A fundamental extension of the ZENO program.

We describe an extension of the ZENO program for polymer and nanoparticle characterization that allows for precise calculation of the virial coefficients, with uncertainty estimates, of polymeric structures described by arbitrary rigid configurations of hard spheres. The probabilistic method of virial computation used for this extension employs a previously developed Mayer-sampling Monte Carlo method with overlap sampling that allows for a reduction of bias in the Monte Carlo averaging. This capability is an extension of ZENO in the sense that the existing program is also based on probabilistic sampling methods and involves the same input file formats describing polymer and nanoparticle structures. We illustrate the extension's capabilities, demonstrate its accuracy, and quantify the efficiency of this extension of ZENO by computing the second, third, and fourth virial coefficients and metrics quantifying the difficulty of their calculation, for model polymeric structures having several different shapes. We obtain good agreement with literature estimates available for some of the model structures considered.

External-Field-Robust Stochastic Magnetic Tunnel Junctions Using a Free Layer with Synthetic Antiferromagnetic Coupling

The stochastic magnetic tunnel junction (MTJ), the resistance of which fluctuates in time between low and high states under thermal fluctuation, is expected to serve as a key element in probabilistic computers. For reliable operation and versatile application, one needs to address the challenge that the relaxation time in each state should be virtually independent of external magnetic fields in the range of, for example, several mT. In this research, we fabricate in-plane easy-axis elliptical stochastic MTJs with a synthetic antiferromagnetic (SAF) free layer and examine the robustness of their properties against external fields while comparing them with stochastic MTJs with a conventional single ferromagnetic structure. We show that the MTJ with a SAF free layer shows more robust relaxation times against fields applied along the easy- and hard-axis directions. The results are reproduced with a macrospin simulation, from which design guidelines for robust stochastic MTJs targeting probabilistic computers are discussed.

Stochastic dynamics of a metal magnon parametron

A magnon parametron is a calculating element that carries binary information by a discretized oscillating phase: 0 and π. Owing to the strong non-linearity of the magnetization dynamics, the oscillation phase flips to another stochastically, which can give a rise to unconventional computing functionalities, including probabilistic computing. Here, we investigated the stochastic dynamics of ferromagnetic-metal magnon parametron, of which the precession phase is discretized into two (0 and π) by parametric pumping of magnons. We found that an AC magnetic field perpendicular to an external field can control the precession phase in the magnon parametron, of which amplitude dependence follows the sigmoid function, a requirement for probabilistic bit operation. We also found that the time scale for flipping between different precession phases grows exponentially as pumping microwave power. Our finding ensures that the magnon parametron can be used as a calculating element for unconventional computing schemes based on bistable systems.

Probabilistic Neural Computing with Stochastic Devices.

The brain has effectively proven a powerful inspiration for the development of computing architectures in which processing is tightly integrated with memory, communication is event-driven, and analog computation can be performed at scale. These neuromorphic systems increasingly show an ability to improve the efficiency and speed of scientific computing and artificial intelligence applications. Herein, it is proposed that the brain's ubiquitous stochasticity represents an additional source of inspiration for expanding the reach of neuromorphic computing to probabilistic applications. To date, many efforts exploring probabilistic computing have focused primarily on one scale of the microelectronics stack, such as implementing probabilistic algorithms on deterministic hardware or developing probabilistic devices and circuits with the expectation that they will be leveraged by eventual probabilistic architectures. A co-design vision is described by which large numbers of devices, such as magnetic tunnel junctions and tunnel diodes, can be operated in a stochastic regime and incorporated into a scalable neuromorphic architecture that can impact a number of probabilistic computing applications, such as Monte Carlo simulations and Bayesian neural networks. Finally, a framework is presented to categorize increasingly advanced hardware-based probabilistic computing technologies.

Efficient Probabilistic Computing with Stochastic Perovskite Nickelates.

Probabilistic computing has emerged as a viable approach to solve hard optimization problems. Devices with inherent stochasticity can greatly simplify their implementation in electronic hardware. Here, we demonstrate intrinsic stochastic resistance switching controlled via electric fields in perovskite nickelates doped with hydrogen. The ability of hydrogen ions to reside in various metastable configurations in the lattice leads to a distribution of transport gaps. With experimentally characterized p-bits, a shared-synapse p-bit architecture demonstrates highly parallelized and energy-efficient solutions to optimization problems such as integer factorization and Boolean satisfiability. The results introduce perovskite nickelates as scalable potential candidates for probabilistic computing and showcase the potential of light-element dopants in next-generation correlated semiconductors.

Model checking hyperproperties for Markov decision processes

We study the problem of formalizing and checking probabilistic hyperproperties for Markov decision processes (MDPs). We introduce the temporal logic HyperPCTL that allows explicit and simultaneous quantification over schedulers as well as probabilistic computation trees. We show that the logic can express important quantitative requirements in security and privacy such as probabilistic noninterference, differential privacy, timing side-channel countermeasures, and probabilistic conformance testing. We show that HyperPCTL model checking over MDPs is in general undecidable, but restricting the domain of scheduler quantification to memoryless non-probabilistic schedulers turns the model checking problem decidable. Subsequently, we propose an SMT-based encoding for model checking this language. Finally, we demonstrate the applicability of our method by providing experimental results for verification, and we show how it can be used to solve even certain synthesis problems.

Probabilistic computing using Cu0.1Te0.9/HfO2/Pt diffusive memristors

A computing scheme that can solve complex tasks is necessary as the big data field proliferates. Probabilistic computing (p-computing) paves the way to efficiently handle problems based on stochastic units called probabilistic bits (p-bits). This study proposes p-computing based on the threshold switching (TS) behavior of a Cu0.1Te0.9/HfO2/Pt (CTHP) diffusive memristor. The theoretical background of the p-computing resembling the Hopfield network structure is introduced to explain the p-computing system. P-bits are realized by the stochastic TS behavior of CTHP diffusive memristors, and they are connected to form the p-computing network. The memristor-based p-bit is likely to be ‘0’ and ‘1’, of which probability is controlled by an input voltage. The memristor-based p-computing enables all 16 Boolean logic operations in both forward and inverted operations, showing the possibility of expanding its uses for complex operations, such as full adder and factorization.

Safe couplings: coupled refinement types

We enhance refinement types with mechanisms to reason about relational properties of probabilistic computations. Our mechanisms, which are inspired from probabilistic couplings, are applicable to a rich set of probabilistic properties, including expected sensitivity, which ensures that the distance between outputs of two probabilistic computations can be controlled from the distance between their inputs. We implement our mechanisms in the type system of Liquid Haskell and we use them to formally verify Haskell implementations of two classic machine learning algorithms: Temporal Difference (TD) reinforcement learning and stochastic gradient descent (SGD). We formalize a fragment of our system for discrete distributions and we prove soundness with respect to a set-theoretical semantics.

An algebraic method to fidelity-based model checking over quantum Markov chains

Fidelity is one of the most widely used quantities in quantum information that measures the distance of two quantum states through a noisy channel, a kind of quantum operations. In this paper, we consider the model of quantum Markov chain (QMC), in which transitions are weighted by super-operators to characterize quantum operations and the initial quantum state is left parametric. A quantum analogy of probabilistic computation tree logic, called QCTL, is introduced to take into account fidelity, instead of probability measure, over QMC. The key to the model checking problem lies in computing the fidelity of the super-operator valued measure specified by a path formula in QCTL. It is minimized over all initial quantum states, which is intended for analyzing the system performance in the worst case. We achieve it by a reduction to quantifier elimination in the existential theory of the reals. The method is absolutely exact, so that model checking QCTL formulas against QMCs is proved to be decidable in exponential time.

Fractional neural sampling as a theory of spatiotemporal probabilistic computations in neural circuits

A range of perceptual and cognitive processes have been characterized from the perspective of probabilistic representations and inference. To understand the neural circuit mechanism underlying these probabilistic computations, we develop a theory based on complex spatiotemporal dynamics of neural population activity. We first implement and explore this theory in a biophysically realistic, spiking neural circuit. Population activity patterns emerging from the circuit capture realistic variability or fluctuations of neural dynamics both in time and in space. These activity patterns implement a type of probabilistic computations that we name fractional neural sampling (FNS). We further develop a mathematical model to reveal the algorithmic nature of FNS and its computational advantages for representing multimodal distributions, a major challenge faced by existing theories. We demonstrate that FNS provides a unified account of a diversity of experimental observations of neural spatiotemporal dynamics and perceptual processes such as visual perception inference, and that FNS makes experimentally testable predictions.

Testing Linear-Invariant Properties

Fix a prime $p$ and a positive integer $R$. We study the property testing of functions $\mathbb F_p^n\to[R]$. We say that a property is testable if there exists an oblivious tester for this property with one-sided error and constant query complexity. Furthermore, a property is proximity oblivious-testable (PO-testable) if the test is also independent of the proximity parameter $\epsilon$. It is known that a number of natural properties such as linearity and being a low degree polynomial are PO-testable. These properties are examples of linear-invariant properties, meaning that they are preserved under linear automorphisms of the domain. Following work of Kaufman and Sudan, the study of linear-invariant properties has been an important problem in arithmetic property testing. A central conjecture in this field, proposed by Bhattacharyya, Grigorescu, and Shapira, is that a linear-invariant property is testable if and only if it is semi subspace-hereditary. We prove two results, the first resolves this conjecture and the second classifies PO-testable properties. (1) A linear-invariant property is testable if and only if it is semi subspace-hereditary. (2) A linear-invariant property is PO-testable if and only if it is locally characterized. Our innovations are two-fold. We give a more powerful version of the compactness argument first introduced by Alon and Shapira. This relies on a new strong arithmetic regularity lemma in which one mixes different levels of Gowers uniformity. This allows us to extend the work of Bhattacharyya, Fischer, Hatami, Hatami, and Lovett by removing the bounded complexity restriction in their work. Our second innovation is a novel recoloring technique called patching. This Ramsey-theoretic technique is critical for working in the linear-invariant setting and allows us to remove the translation-invariant restriction present in previous work.

Query complexity of unitary operation discrimination

Discrimination of unitary operations is fundamental in quantum computation and information. A lot of quantum algorithms including the well-known Deutsch–Jozsa algorithm, Simon’s algorithm, and Grover’s algorithm can essentially be regarded as discriminating among individual, or sets of unitary operations (oracle operators). The problem of discriminating between two unitary operations U and V can be described as: Given X∈{U,V}, determine which one X is. If X is given with multiple copies, then one can design an adaptive procedure that takes multiple queries to X to output the identification result of X. In this paper, we consider the problem: How many queries are required for achieving a desired failure probability ϵ of discrimination between U and V. We prove in a uniform framework: (i) if U and V are discriminated with bound error ϵ , then the number of queries T must satisfy T≥21−4ϵ(1−ϵ)Θ(U†V), and (ii) if they are discriminated with one-sided error ϵ, then there is T≥21−ϵ2Θ(U†V), where ⌈k⌉ denotes the minimum integer not less than k and Θ(W) denotes the length of the smallest arc containing all the eigenvalues of W on the unit circle.

Demonstration of in-plane magnetized stochastic magnetic tunnel junction for binary stochastic neuron

A binary stochastic neuron (BSN) or a probabilistic bit (p-bit) randomly fluctuates between digitized “0” and “1” with a controllable functionality of time-averaged value. Such an unconventional bit is the most essential building block for the recently proposed stochastic neural networks and probabilistic computing. Here, we experimentally implement a magnetic tunnel junction (MTJ) for BSN, with relaxation times on the order of tens of milliseconds that can be modulated by a current-induced spin-transfer torque. The NIST Statistical Test Suite (800-22a) is used to verify true random number generation by the BSN-MTJ device. Our results suggest the possibility of using the artificial BSN MTJ device in neuromorphic applications as well as in a recently proposed probabilistic computing.

Probabilistic Circuit Implementation Based on P-Bits Using the Intrinsic Random Property of RRAM and P-Bit Multiplexing Strategy.

Probabilistic computing is an emerging computational paradigm that uses probabilistic circuits to efficiently solve optimization problems such as invertible logic, where traditional digital computations are difficult to solve. This paper proposes a true random number generator (TRNG) based on resistive random-access memory (RRAM), which is combined with an activation function implemented by a piecewise linear function to form a standard p-bit cell, one of the most important parts of a p-circuit. A p-bit multiplexing strategy is also applied to reduce the number of p-bits and improve resource utilization. To verify the superiority of the proposed probabilistic circuit, we implement the invertible p-circuit on a field-programmable gate array (FPGA), including AND gates, full adders, multi-bit adders, and multipliers. The results of the FPGA implementation show that our approach can significantly save the consumption of hardware resources.

Reliability-based design of geogrid reinforced soil foundation using kriging surrogates

This paper investigates the benefits of using reinforced soil foundations to improve the bearing pressure of shallow foundations on soil using numerical methods. Numerical study of geogrid reinforced soil involves estimation and validation of geogrid properties. Reliability-based design of reinforced soil foundation is performed using kriging surrogates. This involves calibrating and validating a kriging model using samples generated by any deterministic geotechnical numerical model. Surrogate models simplify probabilistic computations and Monte Carlo simulations. The design methodology is applied for a shallow foundation on soils reinforced with multiple geogrid layers. Results demonstrate the possibilities of surrogate modelling to design geogrid reinforced soil foundations and their capability to reduce settlement and improve bearing capacity, thereby reducing foundation area.

PD-L1, VISTA, and CD47 expression and prognosis impact in malignant pleural mesothelioma.

8562 Background: Malignant Pleural Mesothelioma (MPM) has been characterized by an immune suppressive microenvironment. The immune checkpoint (IC) VISTA is notably expressed in MPM, in contrast to other IC proteins such us PD-L1. Recently, CD47 has been described as a possible diagnostic biomarker for MPM, although its impact in prognosis has not been established yet. Methods: This is a retrospective observational study of immunotherapy naïve MPM patients. Immunochemistry (IHC) assessment of PD-L1, VISTA and CD47 protein expression was performed on tissue microarray of 46 surgical samples. Means were compared using Mann-Whitney U test. Correlation was estimated using Pearson’s coefficients. Overall survival (OS) was assessed using Kaplan–Meier curves and Cox proportional hazard models. A two-sided alpha error of 0.05 was used to assess statistical significance. Statistical analysis was conducted with Stata/SE version 16.1. Results: A total of 46 patients, 71.7% (33/46) male, were included in our study. Among them, 77.8% (35/45) had stage IIIB-IV, 84.8% (39/46) had received systemic therapy and 16.7% (7/42) had undergone radical-intent surgery. Asbestos exposure was confirmed in 65,7% (23/35) patients. Regarding the histological subtype, 71.7% (33/46) were epithelioid (Ep) and 13.0% (6/46) non-epithelioid (NEp), including 5 sarcomatoid and 1 biphasic. In IHC analysis, VISTA and CD47 were expressed in 63.0% (29/46) and 58.7% (27/46), respectively, whereas only 28.3% (13/46) patients had positive PD-L1 expression (≥1%). Median expression of VISTA, CD47 and PD-L1 in tumor samples was 41.8 (95% IC 0.5 - 50.7), 26.3 (95% IC 0 - 45.8) and 0 (95% IC 0-0.5), respectively. VISTA and CD47 expression were significantly higher in the Ep subgroup vs. the NEp subgroup (VISTA 39.4% vs 7.2% p = 0.028; CD47 37.3 vs. 0.8 p = 0.01). Additionally, we found a significant positive correlation between VISTA and CD47 protein expression (Pearson's r = 0.55, p < 0.001), which was consistent with the results we found in an independent MPM patient series from TCGA PanCancer Atlas (N = 87) based on RNA expression (r = 0.46; p < 0.001). Median OS, available in 40/46 cases, was 16.6 months (95% CI 12.03-20.43). On multivariate analysis, CD47 ≥1% expression was significantly associated with longer OS (29.7 vs 10.53 months, HR 0.35, [IC 95% 0.14-0.86]; p = 0.02) after adjusting for histological subtype, PDL1 and VISTA expression. In contrast, PD-L1 ≥1% showed a trend towards worse prognosis (10.3 vs 19.3 months), without reaching statistical significance (HR 2.23 [95% IC 0.95-5.23]; p = 0.065). No OS differences were found regarding VISTA expression. Conclusions: To our knowledge, this is the first study to describe VISTA and CD47 correlation in MPM. Moreover, we demonstrate CD47 expression to be an independent prognostic marker in MPM, suggesting C47 may play a key role in tumor biology of MPM, for which further validation and functional studies are necessary.