Algorithmic inference gathers new developments in the statistical inference methods made feasible by the powerful computing devices widely available to any data analyst. Cornerstones in this field are computational learning theory, granular computing, bioinformatics, and, long ago, structural probability (Fraser 1966). The main focus is on the algorithms which compute statistics rooting the study of a random phenomenon, along with the amount of data they must feed on to produce reliable results. This shifts the interest of mathematicians from the study of the distribution laws to the functional properties of the statistics, and the interest of computer scientists from the algorithms for processing data to the information they process. == The Fisher parametric inference problem == Concerning the identification of the parameters of a distribution law, the mature reader may recall lengthy disputes in the mid 20th century about the interpretation of their variability in terms of fiducial distribution (Fisher 1956), structural probabilities (Fraser 1966), priors/posteriors (Ramsey 1925), and so on. From an epistemology viewpoint, this entailed a companion dispute as to the nature of probability: is it a physical feature of phenomena to be described through random variables or a way of synthesizing data about a phenomenon? Opting for the latter, Fisher defines a fiducial distribution law of parameters of a given random variable that he deduces from a sample of its specifications. With this law he computes, for instance "the probability that μ (mean of a Gaussian variable – omeur note) is less than any assigned value, or the probability that it lies between any assigned values, or, in short, its probability distribution, in the light of the sample observed". == The classic solution == Fisher fought hard to defend the difference and superiority of his notion of parameter distribution in comparison to analogous notions, such as Bayes' posterior distribution, Fraser's constructive probability and Neyman's confidence intervals. For half a century, Neyman's confidence intervals won out for all practical purposes, crediting the phenomenological nature of probability. With this perspective, when you deal with a Gaussian variable, its mean μ is fixed by the physical features of the phenomenon you are observing, where the observations are random operators, hence the observed values are specifications of a random sample. Because of their randomness, you may compute from the sample specific intervals containing the fixed μ with a given probability that you denote confidence. === Example === Let X be a Gaussian variable with parameters μ {\displaystyle \mu } and σ 2 {\displaystyle \sigma ^{2}} and { X 1 , … , X m } {\displaystyle \{X_{1},\ldots ,X_{m}\}} a sample drawn from it. Working with statistics S μ = ∑ i = 1 m X i {\displaystyle S_{\mu }=\sum _{i=1}^{m}X_{i}} and S σ 2 = ∑ i = 1 m ( X i − X ¯ ) 2 , where X ¯ = S μ m {\displaystyle S_{\sigma ^{2}}=\sum _{i=1}^{m}(X_{i}-{\overline {X}})^{2},{\text{ where }}{\overline {X}}={\frac {S_{\mu }}{m}}} is the sample mean, we recognize that T = S μ − m μ S σ 2 m − 1 m = X ¯ − μ S σ 2 / ( m ( m − 1 ) ) {\displaystyle T={\frac {S_{\mu }-m\mu }{\sqrt {S_{\sigma ^{2}}}}}{\sqrt {\frac {m-1}{m}}}={\frac {{\overline {X}}-\mu }{\sqrt {S_{\sigma ^{2}}/(m(m-1))}}}} follows a Student's t distribution (Wilks 1962) with parameter (degrees of freedom) m − 1, so that f T ( t ) = Γ ( m / 2 ) Γ ( ( m − 1 ) / 2 ) 1 π ( m − 1 ) ( 1 + t 2 m − 1 ) m / 2 . {\displaystyle f_{T}(t)={\frac {\Gamma (m/2)}{\Gamma ((m-1)/2)}}{\frac {1}{\sqrt {\pi (m-1)}}}\left(1+{\frac {t^{2}}{m-1}}\right)^{m/2}.} Gauging T between two quantiles and inverting its expression as a function of μ {\displaystyle \mu } you obtain confidence intervals for μ {\displaystyle \mu } . With the sample specification: x = { 7.14 , 6.3 , 3.9 , 6.46 , 0.2 , 2.94 , 4.14 , 4.69 , 6.02 , 1.58 } {\displaystyle \mathbf {x} =\{7.14,6.3,3.9,6.46,0.2,2.94,4.14,4.69,6.02,1.58\}} having size m = 10, you compute the statistics s μ = 43.37 {\displaystyle s_{\mu }=43.37} and s σ 2 = 46.07 {\displaystyle s_{\sigma ^{2}}=46.07} , and obtain a 0.90 confidence interval for μ {\displaystyle \mu } with extremes (3.03, 5.65). == Inferring functions with the help of a computer == From a modeling perspective the entire dispute looks like a chicken-egg dilemma: either fixed data by first and probability distribution of their properties as a consequence, or fixed properties by first and probability distribution of the observed data as a corollary. The classic solution has one benefit and one drawback. The former was appreciated particularly back when people still did computations with sheet and pencil. Per se, the task of computing a Neyman confidence interval for the fixed parameter θ is hard: you do not know θ, but you look for disposing around it an interval with a possibly very low probability of failing. The analytical solution is allowed for a very limited number of theoretical cases. Vice versa a large variety of instances may be quickly solved in an approximate way via the central limit theorem in terms of confidence interval around a Gaussian distribution – that's the benefit. The drawback is that the central limit theorem is applicable when the sample size is sufficiently large. Therefore, it is less and less applicable with the sample involved in modern inference instances. The fault is not in the sample size on its own part. Rather, this size is not sufficiently large because of the complexity of the inference problem. With the availability of large computing facilities, scientists refocused from isolated parameters inference to complex functions inference, i.e. re sets of highly nested parameters identifying functions. In these cases we speak about learning of functions (in terms for instance of regression, neuro-fuzzy system or computational learning) on the basis of highly informative samples. A first effect of having a complex structure linking data is the reduction of the number of sample degrees of freedom, i.e. the burning of a part of sample points, so that the effective sample size to be considered in the central limit theorem is too small. Focusing on the sample size ensuring a limited learning error with a given confidence level, the consequence is that the lower bound on this size grows with complexity indices such as VC dimension or detail of a class to which the function we want to learn belongs. === Example === A sample of 1,000 independent bits is enough to ensure an absolute error of at most 0.081 on the estimation of the parameter p of the underlying Bernoulli variable with a confidence of at least 0.99. The same size cannot guarantee a threshold less than 0.088 with the same confidence 0.99 when the error is identified with the probability that a 20-year-old man living in New York does not fit the ranges of height, weight and waistline observed on 1,000 Big Apple inhabitants. The accuracy shortage occurs because both the VC dimension and the detail of the class of parallelepipeds, among which the one observed from the 1,000 inhabitants' ranges falls, are equal to 6. == The general inversion problem solving the Fisher question == With insufficiently large samples, the approach: fixed sample – random properties suggests inference procedures in three steps: === Definition === For a random variable and a sample drawn from it a compatible distribution is a distribution having the same sampling mechanism M X = ( Z , g θ ) {\displaystyle {\mathcal {M}}_{X}=(Z,g_{\boldsymbol {\theta }})} of X with a value θ {\displaystyle {\boldsymbol {\theta }}} of the random parameter Θ {\displaystyle \mathbf {\Theta } } derived from a master equation rooted on a well-behaved statistic s. === Example === You may find the distribution law of the Pareto parameters A and K as an implementation example of the population bootstrap method as in the figure on the left. Implementing the twisting argument method, you get the distribution law F M ( μ ) {\displaystyle F_{M}(\mu )} of the mean M of a Gaussian variable X on the basis of the statistic s M = ∑ i = 1 m x i {\textstyle s_{M}=\sum _{i=1}^{m}x_{i}} when Σ 2 {\displaystyle \Sigma ^{2}} is known to be equal to σ 2 {\displaystyle \sigma ^{2}} (Apolloni, Malchiodi & Gaito 2006). Its expression is: F M ( μ ) = Φ ( m μ − s M σ m ) , {\displaystyle F_{M}(\mu )=\Phi {\left({\frac {m\mu -s_{M}}{\sigma {\sqrt {m}}}}\right)},} shown in the figure on the right, where Φ {\displaystyle \Phi } is the cumulative distribution function of a standard normal distribution. Computing a confidence interval for M given its distribution function is straightforward: we need only find two quantiles (for instance δ / 2 {\displaystyle \delta /2} and 1 − δ / 2 {\displaystyle 1-\delta /2} quantiles in case we are interested in a confidence interval of level δ symmetric in the tail's probabilities) as indicated on the left in the diagram showing the behavior of
Maximum inner-product search
Maximum inner-product search (MIPS) is a search problem, with a corresponding class of search algorithms which attempt to maximise the inner product between a query and the data items to be retrieved. MIPS algorithms are used in a wide variety of big data applications, including recommendation algorithms and machine learning. Formally, for a database of vectors x i {\displaystyle x_{i}} defined over a set of labels S {\displaystyle S} in an inner product space with an inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } defined on it, MIPS search can be defined as the problem of determining a r g m a x i ∈ S ⟨ x i , q ⟩ {\displaystyle {\underset {i\in S}{\operatorname {arg\,max} }}\ \langle x_{i},q\rangle } for a given query q {\displaystyle q} . Although there is an obvious linear-time implementation, it is generally too slow to be used on practical problems. However, efficient algorithms exist to speed up MIPS search. Under the assumption of all vectors in the set having constant norm, MIPS can be viewed as equivalent to a nearest neighbor search (NNS) problem in which maximizing the inner product is equivalent to minimizing the corresponding distance metric in the NNS problem. Like other forms of NNS, MIPS algorithms may be approximate or exact. MIPS search is used as part of DeepMind's RETRO algorithm.
NovelAI
NovelAI is an online cloud-based, SaaS model, and a paid subscription service for AI-assisted storywriting and text-to-image synthesis, originally launched in beta on June 15, 2021, with the image generation feature being implemented later on October 3, 2022. NovelAI is owned and operated by Anlatan, which is headquartered in Wilmington, Delaware. == Features == NovelAI uses GPT-based large language models (LLMs) to generate storywriting and prose. It has several models, such as Calliope, Sigurd, Euterpe, Krake, and Genji, with Genji being a Japanese-language model. The service also offers encrypted servers and customizable editors. For AI art generation, which generates images from text prompts, NovelAI uses a custom version of the source-available Stable Diffusion text-to-image diffusion model called NovelAI Diffusion, which is trained on a Danbooru-based dataset. NovelAI is also capable of generating a new image based on an existing image. The NovelAI terms of service states that all generated content belongs to the user, regardless if the user is an individual or a corporation. Anlatan states that generated images are not stored locally on their servers. == History == On April 28, 2021, Anlatan officially launched NovelAI. On June 15, 2021, Anlatan released their finetuned GPT-Neo-2.7B model from EleutherAI named Calliope, after the Greek Muses. A day later, they released their Opus-exclusive GPT-J-6B finetuned model named Sigurd, after the Norse/Germanic hero. On March 21, 2023, Nvidia and CoreWeave announced Anlatan being one of the first CoreWeave customers to deploy NVIDIA's H100 Tensor Core GPUs for new LLM model inferencing and training. On April 1, 2023, Anlatan added ControlNet features to their text-to-image NovelAI Diffusion model. On May 16, 2023, Anlatan announced that they named their H100 cluster Shoggy, a reference to H.P. Lovecraft's Shoggoths, which was used to pre-train an undisclosed 8192 token context LLM in-house model. == Reception and controversy == Following the implementation of image generation, NovelAI became a widely-discussed topic in Japan, with some online commentators noting that its image synthesis features are very adept at producing close impressions of anime characters, including lolicon and shotacon imagery, while others have expressed concern that it is a paid service reliant on a diffusion model, while the original machine learning training data consists of images used without the consent of the original artists. Attorney Kosuke Terauchi notes that, since a revision of the law in 2018, it is no longer illegal in Japan for machine learning models to scrape copyrighted content from the internet to use as training data; meanwhile, in the United States where NovelAI is based, there is no specific legal framework which regulates machine learning, and thus the fair use doctrine of US copyright law applies instead. Danbooru has posted an official statement in regards to NovelAI's use of the site's content for AI training, expressing that Danbooru is not affiliated with NovelAI, and does not endorse nor condone NovelAI's use of artists' artworks for machine learning. FayerWayer described NovelAI as a service capable of generating hentai. Manga artist Izumi Ū commented that while the manga style art generated by NovelAI is highly accurate, there are still imperfections in the output, although he views these as human-like in a favourable light nonetheless. In response to the topic of NovelAI, Narugami, founder of the Japanese freelance artist commissioning website Skeb, stated on October 5, 2022 that the use of AI image generation is prohibited on the platform since 2018. Illustrations using NovelAI have been posted on social media and illustration posting sites, and by October 13, 2,111 works tagged with #NovelAI were posted on Pixiv. Pixiv has stated that it is not considering a complete elimination of creations that use AI, though it requires AI-generated posts to be marked as such and allows users to filter them out. == Incidents == On October 6, 2022, NovelAI experienced a data breach where its software's source code was leaked.
Frank Hutter
Frank Hutter is a German computer scientist recognized for his contributions to machine learning, particularly in the areas of automated machine learning (AutoML), hyperparameter optimization, meta-learning and tabular machine learning. He is currently a Hector-Endowed Fellow and PI at the ELLIS Institute Tübingen and a Full Professor (W3) for Machine Learning at the Department of Computer Science, University of Freiburg. Hutter is known for his role in establishing AutoML as a key area in artificial intelligence research. == Education and academic career == Frank Hutter received his academic training in computer science at Darmstadt University of Technology, where he completed his Vordiplom (comparable to a BSc) and Hauptdiplom (equivalent to MSc) by 2004. He later pursued his PhD at the University of British Columbia, under the supervision of Profs. Holger Hoos, Kevin Leyton-Brown and Kevin Murphy, where his doctoral thesis, titled "Automated Configuration of Algorithms for Solving Hard Computational Problems," was awarded the CAIAC Doctoral Dissertation Award for the best thesis in Artificial Intelligence completed at a Canadian university in 2009. Hutter did his postdoctoral research at the University of British Columbia, where he worked from 2009 to 2013. In 2013, he moved to the University of Freiburg, initially leading an Emmy Noether Research Group, and in 2017, he was appointed as a Full Professor. His contributions to machine learning have been recognized globally, particularly his work in AutoML and hyperparameter optimization. Overall, Hutter has authored over 180 peer-reviewed publications, which have garnered more than 89,000 citations, reflecting the high impact of his work. == Contributions in AutoML == Hutter's early research laid the groundwork for the field of Automated Machine Learning (AutoML). He has been a key figure in establishing AutoML as a distinct research area. Along with various colleagues, he organized the AutoML workshops from 2014 to 2021, wrote the first book on AutoML and taught the first MOOC on AutoML. He also co-founded the AutoML conference in 2022 and served as its general chair the first two years. He also published prominent works in various subfields of AutoML, such as hyperparameter optimization, neural architecture search, meta-Learning and AutoML systems. He is currently the most highly cited researcher in AutoML. == Contributions in machine learning for tabular data == Hutter has also made many contributions to machine learning for tabular data. He led the development of the first widely adopted AutoML system for tabular data, AutoWEKA, which was published at KDD 2013 and received the test of time award at KDD (2023). Subsequently, he led the development of Auto-sklearn, the first highly used AutoML system for tabular data in Python, and with it, won the first international AutoML challenge and the subsequent second international AutoML challenge, both of which only included tabular data. More recently, he focused on tabular foundation models, including TabPFN, which was published in Nature magazine. In 2024, he also co-founded Prior Labs, the first company focusing on tabular foundation models. == Awards and honors == Hutter has received numerous awards throughout his career. In 2023, he won the KDD Test of Time Award for Research together with Chris Thornton, Holger H. Hoos, and Kevin Leyton-Brown. He has received three grants from the ERC, including the ERC Starting Grant (2016) and ERC Consolidator Grant (2022), as well as an ERC Proof of Concept Grant (2020). In 2021, he became an ELLIS Unit Director and was also recognized as a EurAI Fellow, in addition to receiving the AIJ Prominent Paper Award. Earlier, he was a recipient of the Google Faculty Research Award in 2018. His groundbreaking research was acknowledged early in his career with the IJCAI Distinguished Paper Award in 2013 and the IJCAI/JAIR Best Paper Prize in 2010. == Representative publications == Hutter, F. Kotthoff, L. and Vanschoren, J., editors. Automated machine learning: methods, systems, challenges, Springer Nature, 2019. www.automl.org/book. Feurer, M., Klein, A., Eggensperger, K., Springenberg, T., Blum, M., Hutter, F. Efficient and Robust Automated Machine Learning. In NeurIPS 2015. Loshchilov, I., and Hutter, F. Decoupled weight decay regularization. In ICLR 2018. Zela, A., Elsken, T. ,Saikia, T. ,Marrakschi, Y. ,Brox, T. and Hutter. ,F.Understanding and Robustifying Differentiable Architecture Search. In ICLR 2020. Hollmann, N., Müller, S., Eggensperger, K. and Hutter, F. TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second, In ICLR 2023.
Theano (software)
Theano is a Python library and optimizing compiler for manipulating and evaluating mathematical expressions, especially matrix-valued ones. In Theano, computations are expressed using a NumPy-esque syntax and compiled to run efficiently on either CPU or GPU architectures. == History == Theano is an open source project primarily developed by the Montreal Institute for Learning Algorithms (MILA) at the Université de Montréal. The name of the software references the ancient philosopher Theano, long associated with the development of the golden mean. On 28 September 2017, Pascal Lamblin posted a message from Yoshua Bengio, Head of MILA: major development would cease after the 1.0 release due to competing offerings by strong industrial players. Theano 1.0.0 was then released on 15 November 2017. On 17 May 2018, Chris Fonnesbeck wrote on behalf of the PyMC development team that the PyMC developers will officially assume control of Theano maintenance once the MILA development team steps down. On 29 January 2021, they started using the name Aesara for their fork of Theano. On 29 Nov 2022, the PyMC development team announced that the PyMC developers will fork the Aesara project under the name PyTensor. == Sample code == The following code is the original Theano's example. It defines a computational graph with 2 scalars a and b of type double and an operation between them (addition) and then creates a Python function f that does the actual computation. == Examples == === Matrix Multiplication (Dot Product) === The following code demonstrates how to perform matrix multiplication using Theano, which is essential for linear algebra operations in many machine learning tasks. === Gradient Calculation === The following code uses Theano to compute the gradient of a simple operation (like a neuron) with respect to its input. This is useful in training machine learning models (backpropagation). === Building a Simple Neural Network === The following code shows how to start building a simple neural network. This is a very basic neural network with one hidden layer. === Broadcasting in Theano === The following code demonstrates how broadcasting works in Theano. Broadcasting allows operations between arrays of different shapes without needing to explicitly reshape them.
Wadhwani Institute for Artificial Intelligence
Wadhwani AI, based in Mumbai, Maharashtra, is an independent, non-profit institute. Founded in 2018, it is dedicated to developing Artificial intelligence solutions for social good. Their mission is to build AI-based innovations and solutions for underserved communities in developing countries, for a wide range of domains including agriculture, education, financial inclusion, healthcare, and infrastructure. == History and funding == The institute was founded with a $30 million philanthropic effort by the Wadhwani brothers, Romesh Wadhwani and Sunil Wadhwani. The institute was inaugurated and dedicated to the nation by Narendra Modi, the 14th Prime Minister of India. In 2019, the institute received a $2 million grant from Google.org to create technologies to help reduce crop losses in cotton farming, through integrated pest management. The United States Agency for International Development awarded $2 million to the institute in 2020 to develop tools, using mathematical modeling techniques and digital technologies such as artificial intelligence and machine learning, to forecast COVID-19 disease patterns, estimate resources needed, and plan interventions. == Collaboration == With assistance from Google, the Ministry of Agriculture and Farmers' Welfare and the Wadhwani AI developed Krishi 24/7, the first AI-powered automated agricultural news monitoring and analysis tool. Through better decision-making, Krishi 24/7 will support the identification of valuable news, provide timely notifications, and respond quickly to safeguard farmers' interests and advance sustainable agricultural growth. The application converts news articles into English after scanning them in several languages. It ensures that the ministry is informed in a timely manner about pertinent occurrences that are published online by extracting key information from news items, including the headline, crop name, event type, date, location, severity, summary, and source link. The National Center for Disease Control has effectively implemented a comparable automated surveillance and analysis tool for disease outbreaks.
AI Image Generators Reviews: What Actually Works in 2026
Trying to pick the best AI image generator? An AI image generator is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI image generator slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.