In statistics, adaptive or "variable-bandwidth" kernel density estimation is a form of kernel density estimation in which the size of the kernels used in the estimate are varied depending upon either the location of the samples or the location of the test point. It is a particularly effective technique when the sample space is multi-dimensional. == Rationale == Given a set of samples, { x → i } {\displaystyle \lbrace {\vec {x}}_{i}\rbrace } , we wish to estimate the density, P ( x → ) {\displaystyle P({\vec {x}})} , at a test point, x → {\displaystyle {\vec {x}}} : P ( x → ) ≈ W n h D {\displaystyle P({\vec {x}})\approx {\frac {W}{nh^{D}}}} W = ∑ i = 1 n w i {\displaystyle W=\sum _{i=1}^{n}w_{i}} w i = K ( x → − x → i h ) {\displaystyle w_{i}=K\left({\frac {{\vec {x}}-{\vec {x}}_{i}}{h}}\right)} where n is the number of samples, K is the "kernel", h is its width and D is the number of dimensions in x → {\displaystyle {\vec {x}}} . The kernel can be thought of as a simple, linear filter. Using a fixed filter width may mean that in regions of low density, all samples will fall in the tails of the filter with very low weighting, while regions of high density will find an excessive number of samples in the central region with weighting close to unity. To fix this problem, we vary the width of the kernel in different regions of the sample space. There are two methods of doing this: balloon and pointwise estimation. In a balloon estimator, the kernel width is varied depending on the location of the test point. In a pointwise estimator, the kernel width is varied depending on the location of the sample. For multivariate estimators, the parameter, h, can be generalized to vary not just the size, but also the shape of the kernel. This more complicated approach will not be covered here. == Balloon estimators == A common method of varying the kernel width is to make it inversely proportional to the density at the test point: h = k [ n P ( x → ) ] 1 / D {\displaystyle h={\frac {k}{\left[nP({\vec {x}})\right]^{1/D}}}} where k is a constant. If we back-substitute the estimated PDF, and assuming a Gaussian kernel function, we can show that W is a constant: W = k D ( 2 π ) D / 2 {\displaystyle W=k^{D}(2\pi )^{D/2}} A similar derivation holds for any kernel whose normalising function is of the order hD, although with a different constant factor in place of the (2 π)D/2 term. This produces a generalization of the k-nearest neighbour algorithm. That is, a uniform kernel function will return the KNN technique. There are two components to the error: a variance term and a bias term. The variance term is given as: e 1 = P ∫ K 2 n h D {\displaystyle e_{1}={\frac {P\int K^{2}}{nh^{D}}}} . The bias term is found by evaluating the approximated function in the limit as the kernel width becomes much larger than the sample spacing. By using a Taylor expansion for the real function, the bias term drops out: e 2 = h 2 n ∇ 2 P {\displaystyle e_{2}={\frac {h^{2}}{n}}\nabla ^{2}P} An optimal kernel width that minimizes the error of each estimate can thus be derived. == Use for statistical classification == The method is particularly effective when applied to statistical classification. There are two ways we can proceed: the first is to compute the PDFs of each class separately, using different bandwidth parameters, and then compare them as in Taylor. Alternatively, we can divide up the sum based on the class of each sample: P ( j , x → ) ≈ 1 n ∑ i = 1 , c i = j n w i {\displaystyle P(j,{\vec {x}})\approx {\frac {1}{n}}\sum _{i=1,c_{i}=j}^{n}w_{i}} where ci is the class of the ith sample. The class of the test point may be estimated through maximum likelihood.
Time-inhomogeneous hidden Bernoulli model
Time-inhomogeneous hidden Bernoulli model (TI-HBM) is an alternative to hidden Markov model (HMM) for automatic speech recognition. Contrary to HMM, the state transition process in TI-HBM is not a Markov-dependent process, rather it is a generalized Bernoulli (an independent) process. This difference leads to elimination of dynamic programming at state-level in TI-HBM decoding process. Thus, the computational complexity of TI-HBM for probability evaluation and state estimation is O ( N L ) {\displaystyle O(NL)} (instead of O ( N 2 L ) {\displaystyle O(N^{2}L)} in the HMM case, where N {\displaystyle N} and L {\displaystyle L} are number of states and observation sequence length respectively). The TI-HBM is able to model acoustic-unit duration (e.g. phone/word duration) by using a built-in parameter named survival probability. The TI-HBM is simpler and faster than HMM in a phoneme recognition task, but its performance is comparable to HMM. For details, see [1] or [2].
View synthesis
In computer graphics, view synthesis, or novel view synthesis, is a task which consists of generating images of a specific subject or scene from a specific point of view, when the only available information is pictures taken from different points of view. This task was only recently (late 2010s – early 2020s) tackled with significant success, mostly as a result of advances in machine learning. Notable successful methods are Neural radiance fields and 3D Gaussian Splatting. Applications of view synthesis are numerous, one of them being Free view point television. The technique has also been applied to real-estate marketing, where novel views of a listing's interior are generated from a limited set of photographs for use in virtual home staging.
Screen space ambient occlusion
Screen space ambient occlusion (SSAO) is a computer graphics technique for efficiently approximating the ambient occlusion effect in real time. It was developed by Vladimir Kajalin while working at Crytek and was used for the first time in 2007 by the video game Crysis, also developed by Crytek. == Implementation == The algorithm is implemented as a pixel shader, analyzing the scene depth buffer which is stored in a texture. For every pixel on the screen, the pixel shader samples the depth values around the current pixel and tries to compute the amount of occlusion from each of the sampled points. In its simplest implementation, the occlusion factor depends only on the depth difference between sampled point and current point. Without additional smart solutions, such a brute force method would require about 200 texture reads per pixel for good visual quality. This is not acceptable for real-time rendering on current graphics hardware. In order to get high quality results with far fewer reads, sampling is performed using a randomly rotated kernel. The kernel orientation is repeated every N screen pixels in order to have only high-frequency noise in the final picture. In the end this high frequency noise is greatly removed by a NxN post-process blurring step taking into account depth discontinuities (using methods such as comparing adjacent normals and depths). Such a solution allows a reduction in the number of depth samples per pixel to about 16 or fewer while maintaining a high quality result, and allows the use of SSAO in soft real-time applications like computer games. Compared to other ambient occlusion solutions, SSAO has the following advantages: Independent from scene complexity. No data pre-processing needed, no loading time and no memory allocations in system memory. Works with dynamic scenes. Works in the same consistent way for every pixel on the screen. No CPU usage – it can be executed completely on the GPU. May be easily integrated into any modern graphics pipeline. SSAO also has the following disadvantages: Rather local and in many cases view-dependent, as it is dependent on adjacent texel depths which may be generated by any geometry whatsoever. Hard to correctly smooth/blur out the noise without interfering with depth discontinuities, such as object edges (the occlusion should not "bleed" onto objects). Because SSAO operates only on the current depth buffer, it can miss occluding geometry that is not rasterized into the z-buffer and may produce undersampling-related artifacts.
PenTile matrix family
PenTile matrix is a family of patented subpixel matrix schemes used in electronic device displays. PenTile is a trademark of Samsung. PenTile matrices are used in AMOLED and LCD displays. These subpixel layouts are specifically designed to operate with proprietary algorithms for subpixel rendering embedded in the display driver, allowing plug and play compatibility with conventional RGB (Red-Green-Blue) stripe panels. == Overview == "PenTile Matrix" (a neologism from penta-, meaning "five" in Greek and tile) describes the geometric layout of the prototypical subpixel arrangement developed in the early 1990s. The layout consists of a quincunx comprising two red subpixels, two green subpixels, and one central blue subpixel in each unit cell. It was inspired by biomimicry of the human retina, which has nearly equal numbers of L and M type cone cells, but significantly fewer S cones. As the S cones are primarily responsible for perceiving blue colors, which do not appreciably affect the perception of luminance, reducing the number of blue subpixels with respect to the red and green subpixels in a display does not reduce the image quality. However, the layout may cause color leakage image distortion, which can be reduced by filters. In some cases the layout causes reduced moiré and blockiness compared to conventional RGB layouts. The PenTile layout is specifically designed to work with and be dependent upon subpixel rendering that uses only one and a quarter subpixel per pixel, on average, to render an image. That is, that any given input pixel is mapped to either a red-centered logical pixel, or a green-centered logical pixel. === History === PenTile was invented by Candice H. Brown Elliott, for which she was awarded the Society for Information Display's Otto Schade Prize in 2014. The technology was licensed by the company Clairvoyante from 2000 until 2008, during which time several prototype PenTile displays were developed by a number of Asian liquid crystal display (LCD) manufacturers. In March 2008, Samsung Electronics acquired Clairvoyante's PenTile IP assets. Samsung then funded a new company, Nouvoyance, Inc. to continue development of the PenTile technology. == PenTile RGBG == PenTile RGBG layout used in AMOLED and plasma displays uses green pixels interleaved with alternating red and blue pixels. The human eye is most sensitive to green, especially for high resolution luminance information. The green subpixels are mapped to input pixels on a one-to-one basis. The red and blue subpixels are subsampled, reconstructing the chroma signal at a lower resolution. The luminance signal is processed using adaptive subpixel rendering filters to optimize reconstruction of high spatial frequencies from the input image, wherein the green subpixels provide the majority of the reconstruction. The red and blue subpixels are capable of reconstructing the horizontal and vertical spatial frequencies, but not the highest of the diagonal. Diagonal high spatial frequency information in the red and blue channels of the input image are transferred to the green subpixels for image reconstruction. Thus the RG-BG scheme creates a color display with one third fewer subpixels than a traditional RGB-RGB scheme but with the same measured luminance display resolution. This is similar to the Bayer filter commonly used in digital cameras. === Devices === As of 2021, "almost all" OLED screens in portable consumer devices use some form of Pentile subpixel layout. == PenTile RGBW == PenTile RGBW technology, used in LCD, adds an extra subpixel to the traditional red, green and blue subpixels that is a clear area without color filtering material and with the only purpose of letting backlight come through, hence W for white. This makes it possible to produce a brighter image compared to an RGB-matrix while using the same amount of power, or produce an equally bright image while using less power. The PenTile RGBW layout uses each red, green, blue and white subpixel to present high-resolution luminance information to the human eyes' red-sensing and green-sensing cone cells, while using the combined effect of all the color subpixels to present lower-resolution chroma (color) information to all three cone cell types. Combined, this optimizes the match of display technology to the biological mechanisms of human vision. The layout uses one third fewer subpixels for the same resolution as the RGB stripe (RGB-RGB) layout, in spite of having four color primaries instead of the conventional three, using subpixel rendering combined with metamer rendering. Metamer rendering optimizes the energy distribution between the white subpixel and the combined red, green, and blue subpixels: W <> RGB, to improve image sharpness. The display driver chip has an RGB to RGBW color vector space converter and gamut mapping algorithm, followed by metamer and subpixel rendering algorithms. In order to maintain saturated color quality, to avoid simultaneous contrast error between saturated colors and peak white brightness, while simultaneously reducing backlight power requirements, the display backlight brightness is under control of the PenTile driver engine. When the image is mostly desaturated colors, those near white or grey, the backlight brightness is significantly reduced, often to less than 50% peak, while the LCD levels are increased to compensate. When the image has very bright saturated colors, the backlight brightness is maintained at higher levels. The PenTile RGBW also has an optional high-brightness mode that doubles the brightness of the desaturated color image areas, such as black-and-white text, for improved outdoor viewability. === Devices === Motorola MC65 Motorola ES55 Motorola ES400 Motorola Atrix 4G Samsung Galaxy Note 10.1 2014 version Lenovo Yoga 2 Pro Lenovo Yoga 3 Pro HP ENVY TouchSmart 14-k022tx Sleekbook MSI GS60 Ghost Pro 4K Lenovo IdeaPad Y50 4K Asus ZenBook UX303LN 4K Asus ZenBook Pro UX501JW LG UH7500/6500/6100 LG ThinQ G7/G7+ Oculus Quest 1 == Controversy == An ongoing controversy regarding the definition or measurement of resolution of color subpixelated flat panel displays led many people to question the resolution claims of PenTile display products. Journalists have noted that in "just about every flat-panel TV in existence, each pixel is composed of one red, one green, and one blue subpixel (RGB), all of uniform size". In traditional flat-panel screens, the resolution is defined by the number of red, green, and blue subpixels, in groups of three, in an array in each axis. As a result, each pixel or group of subpixels can render any colour on the screen, regardless of neighbouring pixels. This is not the case with PenTile screens. The Video Electronics Standards Association (VESA) method of measuring and defining resolution in color displays is to measure the contrast of line pairs, requiring a minimum of 50% Michelson contrast for displays intended for rendering text. The developers of PenTile displays use this VESA criterion for contrast of line pairs to calculate the resolutions specified. In the RGBG layout the alternate red and blue subpixels are 'shared' or sub-sampled with neighboring pixels. Due to the one third lower subpixel density on PenTile displays the pixel structure may be more visible when compared to RGB stripe displays with the same pixel density. The loss of subpixels for a given resolution specification has led some journalists to describe the use of PenTile as "shady practice" and "sort of cheating". For a given size and resolution specification, the PenTile screen can appear grainy, pixelated, speckled, with blurred text on some saturated colors and backgrounds when compared to RGB stripe color. This effect is understood to be caused by the restriction of the number of subpixels that may participate in the image reconstruction when colors are highly saturated to primaries. In the RGBW case, this is caused as the W subpixel will not be available in order to maintain the saturated color. In the RGBG case, this effect will occur when the color boundary is primarily red or blue, as the fully populated (one green per pixel) sub-pixel cannot contribute. For all other cases, text and especially full color images are effectively reconstructed. == Advantages and disadvantages == The PenTile layout reduces the number of subpixels needed to create a specified resolution. Consequently it is possible to achieve an HD resolution on a PenTile AMOLED screen at lower cost than other technologies, and most reviewers note that "300 ppi" (as per VESA - not full pixels) resolution displays (such as Samsung Galaxy S III) make the PenTile effect less obvious than lower resolution PenTile displays (Droid Razr). The second advantage is lower power consumption: the HTC One S's use of a PenTile display makes it more energy efficient and thinner than equivalent LCD screens, giving it better battery life than the HTC One X's IPS LCD. A PenTile AMOLED screen is also
Rhetorical structure theory
Rhetorical structure theory (RST) is a theory of text organization that describes relations that hold between parts of text. It was originally developed by William Mann, Sandra Thompson, Christian M. I. M. Matthiessen and others at the University of Southern California's Information Sciences Institute (ISI) and defined in a 1988 paper. The theory was developed as part of studies of computer-based text generation. Natural language processing researchers later began using RST in automatic summarization and other applications. It explains coherence by postulating a hierarchical, connected structure of texts, which are labeled using a small, predefined inventory of relation types - for example, one part of a text may provide an elaboration on another part, provide background or specify a cause for another. In the 2000s, following the release of the first large-scale dataset implementing the theory, the RST Discourse Treebank (RST-DT), Daniel Marcu demonstrated the feasibility of practical applications of RST to discourse parsing and summarization at ISI. Originally limited to written text, subsequent work in the 2010s expanded RST to spoken language analysis, and the framework has been applied to a variety of languages including Farsi, German, Mandarin Chinese, Russian and Spanish. Following the introduction of Transformers, LLMs have been applied to automatic RST parsing, with results approaching human performance on parsing text in English. == Rhetorical relations == Rhetorical relations, also called coherence or discourse relations, are paratactic (coordinate) or hypotactic (subordinate) relations that hold across two or more text spans. The logical arrangement of relations in a text contributes to its coherence by connecting different propositions in a relational structure. RST using rhetorical relations provides a systematic way for an analyst to analyze the underlying intention of a text. The analysis is usually built by reading the text and constructing a tree using the relations. The following example is a title and summary, appearing at the top of an article in Scientific American magazine (adapted from Ramachandran and Anstis, 1986). The original text, broken into numbered units, is: [Title:] The Perception of Apparent Motion [Abstract:] When the motion of an intermittently seen object is ambiguous the visual system resolves confusion by applying some tricks that reflect a built-in knowledge of properties of the physical world. In the figure, the numbers 1-5 show the corresponding units from the text above. Unit 5 provides an "elaboration" on unit 4, and therefore constitutes a less prominent satellite of unit 4, which acts as a nucleus for the relation. Units 4-5 form a relation "Means", explaining the means by which the visual system resolves confusion. Unit 3 is the Central Discourse Unit (CDU) of the text, since all units point to it directly or indirectly. Similarly units 1 and 2 form "preparation" and "circumstance" relations relative to their nuclei. Groups of units which serve as a satellite or nucleus together are called complex discourse units, and always span a set of adjacent EDUs. == Nuclearity in discourse == RST establishes two different types of units. Nuclei are considered as the most important parts of text whereas satellites contribute to the nuclei and are secondary. Nucleus contains basic information and satellite contains additional information about nucleus. The satellite is often incomprehensible without nucleus, whereas a text where satellites have been deleted can be understood to a certain extent. == Hierarchy in the analysis == RST relations are applied recursively in a text, until all units in that text are constituents in an RST relation. The result of such analyses is that RST structure are typically represented as trees, with one top level relation that encompasses other relations at lower levels. == Why RST? == From linguistic point of view, RST proposes a different view of text organization than most linguistic theories. RST points to a tight relation between relations and coherence in text From a computational point of view, it provides a characterization of text relations that has been implemented in different systems and for applications as text generation and summarization. == In design rationale == Computer scientists Ana Cristina Bicharra Garcia and Clarisse Sieckenius de Souz have used RST as the basis of a design rationale system called ADD+. In ADD+, RST is used as the basis for the rhetorical organization of a knowledge base, in a way comparable to other knowledge representation systems such as issue-based information system (IBIS). Similarly, RST has been used in representation schemes for argumentation.
Two-phase locking
In databases and transaction processing, two-phase locking (2PL) is a pessimistic concurrency control method that guarantees conflict-serializability. It is also the name of the resulting set of database transaction schedules (histories). The protocol uses locks, applied by a transaction to data, which may block (interpreted as signals to stop) other transactions from accessing the same data during the transaction's life. By the 2PL protocol, locks are applied and removed in two phases: Expanding phase: locks are acquired and no locks are released. Shrinking phase: locks are released and no locks are acquired. Two types of locks are used by the basic protocol: Shared and Exclusive locks. Refinements of the basic protocol may use more lock types. Using locks that block processes, 2PL, S2PL, and SS2PL may be subject to deadlocks that result from the mutual blocking of two or more transactions. == Read and write locks == Locks are used to guarantee serializability. A transaction is holding a lock on an object if that transaction has acquired a lock on that object which has not yet been released. For 2PL, the only used data-access locks are read-locks (shared locks) and write-locks (exclusive locks). Below are the rules for read-locks and write-locks: A transaction is allowed to read an object if and only if it is holding a read-lock or write-lock on that object. A transaction is allowed to write an object if and only if it is holding a write-lock on that object. A schedule (i.e., a set of transactions) is allowed to hold multiple locks on the same object simultaneously if and only if none of those locks are write-locks. If a disallowed lock attempts on being held simultaneously, it will be blocked. == Variants == Note that all conflict serializable schedules are also view serializable (but not vice-versa). === Two-phase locking === According to the two-phase locking protocol, each transaction handles its locks in two distinct, consecutive phases during the transaction's execution: Expanding phase (aka Growing phase): locks are acquired and no locks are released (the number of locks can only increase). Shrinking phase (aka Contracting phase): locks are released and no locks are acquired. The two phase locking rules can be summarized as: each transaction must never acquire a lock after it has released a lock. The serializability property is guaranteed for a schedule with transactions that obey this rule. Typically, without explicit knowledge in a transaction on end of phase 1, the rule is safely determined only when a transaction has completed processing and requested commit. In this case, all the locks can be released at once (phase 2). === Conservative two-phase locking === Conservative two-phase locking (C2PL) differs from 2PL in that transactions obtain all the locks they need before the actual execution begins. This is to ensure that a transaction that already holds some locks will not block waiting for other locks. C2PL prevents deadlocks. In cases of heavy lock contention, C2PL reduces the time locks are held on average, relative to 2PL and Strict 2PL, because transactions that hold locks are never blocked. In light lock contention, C2PL holds more locks than is necessary, because it is difficult to predict which locks will be needed in the future, thus leading to higher overhead. A C2PL transaction will not obtain any locks if it cannot obtain all the locks it needs in its initial request. Furthermore, each transaction needs to declare its read and write set (the data items that will be read/written), which is not always possible. Because of these limitations, C2PL is not used very frequently. === Strict two-phase locking === To comply with the strict two-phase locking (S2PL) protocol, a transaction needs to comply with 2PL, and release its write (exclusive) locks only after the transaction has ended (i.e., either committed or aborted). On the other hand, read (shared) locks are released regularly during the shrinking phase. Unlike 2PL, S2PL provides strictness (a special case of cascade-less recoverability). This protocol is not appropriate in B-trees because it causes Bottleneck (while B-trees always starts searching from the parent root). === Strong strict two-phase locking === or Rigorousness, or Rigorous scheduling, or Rigorous two-phase locking To comply with strong strict two-phase locking (SS2PL), a transaction's read and write locks are released only after that transaction has ended (i.e., either committed or aborted). A transaction obeying SS2PL has only a phase 1 and lacks a phase 2 until the transaction has completed. Every SS2PL schedule is also an S2PL schedule, but not vice versa.